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Recent no‐go theorems have ruled out four‐dimensional classical de Sitter vacua in heterotic string theory. On the other hand, the absence of a well‐defined Wilsonian effective action and other related phenomena also appear to rule out such time‐dependent vacua with de Sitter isometries, even in the presence of quantum corrections. In this note, the authors argued that a four‐dimensional de Sitter space can still exist in SO(32)$SO(32)$ heterotic string theory as a Glauber–Sudarshan state, i.e., as an excited state, over a supersymmetric Minkowski background, albeit within a finite temporal domain. Borel resummation and resurgence play a crucial role in constructing such a state in the Hilbert space of heterotic theory governed entirely by the IR degrees of freedom. [ABSTRACT FROM AUTHOR]

We perform a systematic analysis of the one‐loop effective potential of pure d=5$d=5$ supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential V1$V_1$ in the full compactified theory and its counterpart V1,red$V_{1,red}$ in the reduced theory. We confirm that V1$V_1$ is finite for any N>0$N>0$, in contrast to V1,red$V_{1,red}$. We find that for broken N=8$N=8$ supergravity V1$V_1$ is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results. We perform a systematic analysis of the one‐loop effective potential of pure d=5$d=5$ supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential V1$V_1$ in the full compactified theory and its counterpart V1,red$V_{1,red}$ in the reduced theory. We confirm that V1$V_1$ is finite for any N>0$N>0$, in contrast to V1,red$V_{1,red}$. We find that for broken N = 8 supergravity V1$V_1$ is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results. [ABSTRACT FROM AUTHOR]

Chirality is one of the fundamental properties of molecules traditionally constructed from atoms. Here, we report for the first time the successful construction of asymmetric chiral structures utilizing highly symmetric endohedral metallofullerene superatoms based on their own bonding properties. Specifically, stable mirror‐symmetric sinister and rectus structures are obtained by selecting a superatom capable of forming four chemical bonds as the chiral center. Further analysis shows that the chiral vibration frequency of superatomic assemblies can be as low as a few wavenumbers, which greatly expands the range of chiral spectra compared to atom‐based molecules. We term this type of chirality based on superatoms as "superatomic‐based chirality". It is anticipated that this work will significantly expand the variety of chiral structures at the atomic level. [ABSTRACT FROM AUTHOR]

Avatars of T‐duality within Sen's formalism for self‐dual field strengths in various dimensions are studied. This formalism is shown to naturally accommodate the T‐duality relation between Type IIA/IIB theories when compactified on a circle without the need for imposing the self‐duality constraint by hand, as is usually done. The study of this formalism is continued on two‐dimensional target spacetimes and its study as a worldsheet theory is initiated. In particular, it is shown that Sen's action provides a natural worldsheet‐based understanding of twisted and asymmetrically twisted strings. Finally, it is shown that the TT¯$\mathrm{T}\bar{\mathrm{T}}$‐deformed theory of left‐ and right‐chiral bosons described in Sen's formalism possesses a scaling limit that is related via field‐theoretic T‐duality to a recently studied integrable deformation of quantum mechanics. [ABSTRACT FROM AUTHOR]

Universal factors associated with the emission of a soft boson in gauge theories and gravity, formulated in the light‐cone gauge, are presented. The inverse‐soft method, for constructing higher‐point amplitudes from lower‐point ones, using these factors is reviewed. These ideas are then examined in (light‐cone) superspace and applied to both the N=4$\mathcal {N}=4$ super Yang–Mills and N=8$\mathcal {N}=8$ supergravity theories. One highlight is a compact result for the quartic interaction vertex in N=8$\mathcal {N}=8$ supergravity, a crucial ingredient for finiteness analyses. Universal factors associated with the emission of a soft boson in gauge theories and gravity, formulated in the light‐cone gauge, are presented. The inverse‐soft method, for constructing higher‐point amplitudes from lower‐point ones, using these factors is reviewed. These ideas are then examined in (light‐cone) superspace and applied to both the N=4$\mathcal{N} = 4$ super Yang–Mills and N=8$\mathcal{N} = 8$ supergravity theories. One highlight is a compact result for the quartic interaction vertex in N=8$\mathcal{N} = 8$ supergravity, a crucial ingredient for finiteness analyses. [ABSTRACT FROM AUTHOR]

The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels. Quantum degeneracies of spherically symmetric stationary BPS black holes are given by the Fourier coefficients of modular forms of exceptional group E7(−25)$E_{7(-25)}$. Their charges take values in the lattice defined by the exceptional Jordan algebra over integral octonions. The quantum degeneracies of rank 1 and rank 2 BPS black holes are given by the Fourier coefficients of singular modular forms E4(Z)$E_4(Z)$ and E8(Z)$E_8(Z)$. The rank 3 (large) BPS black holes will be studied elsewhere. Following the work of N. Elkies and B. Gross on embeddings of cubic rings A into the exceptional Jordan algebra we show that the quantum degeneracies of rank 1 black holes described by such embeddings are given by the Fourier coefficients of the Hilbert modular forms (HMFs) of SL(2,A)$SL(2,A)$. If the discriminant of the cubic ring A is D=p2$D=p^2$ with p a prime number then the isotropic lines in the 24 dimensional orthogonal complement of A define a pair of Niemeier lattices which can be taken as charge lattices of some BPS black holes. The current status of the searches for the M/superstring theoretic origins of the octonionic magical supergravity is also reviewed. [ABSTRACT FROM AUTHOR]

Large classes of multi‐center supergravity solutions have been constructed in the study of supersymmetric black holes and their microstates. Many smooth multi‐center solutions have the same charges as supersymmetric black holes, with all centers deep inside a long black‐hole‐like throat. These configurations are constrained by regularity, absence of closed timelike curves, and charge quantization. Due to these constraints, constructing explicit solutions with several centers in generic arrangements, and with all parameters in physically relevant ranges, is a hard task. In this work, an optimization algorithm, based on evolutionary algorithms and Bayesian optimization is presented, that systematically constructs numerical solutions satisfying all constraints. Explicit examples of novel five‐center and seven‐center machine‐precision solutions are exhibited. [ABSTRACT FROM AUTHOR]

Euclidean Wilson loops for BMN Plane Wave Matrix Models is computed. The stringy counterpart of these Wilson loops corresponds to various semi‐classical open string embedding that probe a class of half BPS geometries in Type IIA supergravity. These geometries fall under the general category of Lin‐Lunin and Maldacena (LLM). As a special class of solutions within the LLM category, Wilson operators corresponding to the non‐Abelian T dual (NATD) of AdS5×S5$ AdS_5 \times S^5$ is constructed. The analysis shows close agreement between matrix model and string theory calculations. [ABSTRACT FROM AUTHOR]

The presence of a nonvanishing totally antisymmetric (super)torsion, equivalent to an axial vector, and higher forms in the "new minimal" and "old minimal" off‐shell formulations of N=1$\mathcal {N}=1$, D=4$D=4$ supergravity is elaborated. The geometric superspace approach and study both the geometric Lagrangian and the off‐shell closure of the Bianchi identities in this framework, showing how the aforementioned axial vector torsion contributes to both the new and the old minimal set of auxiliary fields is adopted. In particular, to reproduce (a variant of) the old minimal set within the geometric setup, two real auxiliary 3‐form potentials. The presence of a nonvanishing totally antisymmetric (super)torsion, equivalent to an axial vector, and higher forms in the "new minimal" and "old minimal" off‐shell formulations of N=1$\mathcal {N}=1$, D=4$D=4$ supergravity is elaborated. The geometric superspace approach and study both the geometric Lagrangian and the off‐shell closure of the Bianchi identities in this framework, showing how the aforementioned axial vector torsion contributes to both the new and the old minimal set of auxiliary fields is adopted. In particular, to reproduce (avariant of) the old minimal set within the geometric setup, two real auxiliary 3‐form potentials. [ABSTRACT FROM AUTHOR]

We study the formation of primordial black holes (PBH) in the Starobinsky supergravity coupled to the nilpotent superfield describing Volkov–Akulov goldstino. By using the no‐scale Kähler potential and a polynomial superpotential, we find that under certain conditions our model can describe effectively single‐field inflation with the ultra‐slow‐roll phase that appears near a critical (near‐inflection) point of the scalar potential. This can lead to the formation of PBH as part of (or whole) dark matter, while keeping the inflationary spectral tilt and the tensor‐to‐scalar ratio in good agreement with the current cosmic microwave background (CMB) bounds. After inflation, supersymmetry is spontaneously broken at the inflationary scale with the vanishing cosmological constant. This paper deals with the thermodynamics, Joule‐Thomson expansion and optical behaviour of a Reissner‐Nordström‐anti‐de Sitter black hole in Rastall gravity surrounded by a quintessence field. The black hole solution obtained in this framework is different from a corresponding black hole in General Relativity. The black hole metric function, as well as the Hawking temperature, is affected by the presence of energy‐momentum conservation violation. The presence of energy‐momentum conservation violation also affects the isenthalpic and inversion temperature curves, and with an increase in the Rastall parameter, the inversion temperature rises slowly. The impacts of other parameters, such as charge, structural constant etc., are investigated and compared. The black hole shadow, as well as the energy emission rate of the black hole, decreases with an increase in the Rastall parameter. Hence, the black holes evaporate slowly in presence of energy‐momentum conservation violation. [ABSTRACT FROM AUTHOR]

We examine the vacua of the scalar potential of the effective 4‐d action, obtained after the dimensional reduction of the 10‐d N=1$\mathcal {N}=1$ heterotic supergravity coupled to an N=1$\mathcal {N}=1$ Yang‐Mills sector. The (Coset Space) dimensional reduction takes place over the three 6‐d nearly‐Kähler manifolds, namely the homogeneous 6‐d non‐symmetric coset spaces, G2/SU(3)$G_2/SU(3)$, Sp4/SU(2)×U(1)$Sp_4/SU(2)\times U(1)$ and SU(3)/U(1)×U(1)$SU(3)/U(1)\times U(1)$. The current work consists a complete catalogue of the kinds of vacua of theories obtained after the reduction of the heterotic string over the 6‐d non‐symmetric coset spaces and, moreover, a contribution to the dialogue of the possibility to result with non‐AdS vacua in the framework of string theories. We examine the vacua of the scalar potential of the effective 4‐d action, obtained after the dimensional reduction of the 10‐d N=1$\mathcal {N}=1$ heterotic supergravity coupled to an N=1$\mathcal {N}=1$ Yang‐Mills sector. The (Coset Space) dimensional reduction takes place over the three 6‐d nearly‐Kähler manifolds, namely the homogeneous 6‐d non‐symmetric coset spaces, G2/SU(3)$G_2/SU(3)$, Sp4/SU(2)×U(1)$Sp_4/SU(2)\times U(1)$. The current work consists a complete catalogue of the kinds of vacua of theories obtained after the reduction of the heterotic string over the 6‐d non‐symmetric coset spaces and, moreover, a contribution to the dialogue of the possibility to result with non‐AdS vacua in the framework of string theories. [ABSTRACT FROM AUTHOR]

In this paper, minimal supersymmetric AdS3 solutions on G2‐orientifolds of type IIA and IIB supergravity are studied. These are obtained by techniques of the bispinor formalism. A straightforward argument is derived against AdS3 solutions in massless type IIA string theory on such G2‐backgrounds. Furthermore, it is shown that some of the AdS3 solutions in massive type IIA do admit a separation of scales, whereas the same cannot be said for the type IIB vacua. Finally, a formula for the 3d superpotential in the bispinor language is given that is valid for both type IIA and type IIB configurations. It is shown that the supersymmetry conditions of this superpotential lead back to the bispinor equations. [ABSTRACT FROM AUTHOR]

Bayan Obo ore has abundant rare earth (RE) reserves, and RE elements (REEs) are mainly transferred into the RE‐bearing slag. However, the utilization of RE‐bearing slag is greatly limited due to the serious lack and ambiguity of RE crystals. In this study, in situ separation of RE crystals from RE‐bearing slag via supergravity was developed, and the high‐purity crystals of britholite with various REEs contents were selectively separated from the CaO–SiO2–CaF2–P2O5–Ce2O3 system with a high REEs recovery ratio of 95.58%–98.65%. On this basis, the chemical formula, the crystal structure, and the formation mechanism of britholite were characterized from the high‐purity crystals through a combination of the Rietveld refinement and DFT calculation. It was found that the britholite was verified to be evolved from Ca5(PO4)3F, there would be an SiO44− instead of a PO43− when a Ce3+ replaced a Ca2+, the chemical formula changed from Ca5(PO4)3F to Ca4.377Ce0.623Si0.6P2.4O12F, Ca3.956Ce1.044Si1.01P1.99O12F, and Ca3.176Ce1.824Si1.93P1.07O12F with the increase of REEs content, and the substitution range of REEs was between 0 and 2. This study supplements some necessary basic data of RE crystals, which provides the theoretical reference for efficient recovery of RE resources and sustainable utilization of RE‐bearing slag. [ABSTRACT FROM AUTHOR]

Use of supergravity equations in astronomy and late‐universe cosmology is often criticized on three grounds: (i) phenomenological success usually depends on the supergravity form for the scalar potential applying at the relevant energies; (ii$ii$) the low‐energy scalar potential is extremely sensitive to quantum effects involving very massive particles and so is rarely well‐approximated by classical calculations of its form; and (iii$iii$) almost all Standard Model particles count as massive for these purposes and none of these are supersymmetric. Why should Standard Model loops preserve the low‐energy supergravity form even if supersymmetry is valid at energies well above the electroweak scale? We use recently developed tools for coupling supergravity to non‐supersymmetric matter to estimate the loop effects of heavy non‐supersymmetric particles on the low‐energy effective action, and provide evidence that the supergravity form is stable against integrating out such particles (and so argues against the above objection). This suggests an intrinsically supersymmetric picture of Nature where supersymmetry survives to low energies within the gravity sector but not the visible sector (for which supersymmetry is instead non‐linearly realized). We explore the couplings of both sectors in this picture and find that the presence of auxiliary fields in the gravity sector makes the visible sector share many features usually attributed to linearly realized supersymmetry although (unlike for the MSSM) a second Higgs doublet is not required for all Yukawa couplings to be non‐vanishing and changes the dimension of the operator generating the Higgs mass. We discuss the naturalness of this picture and some of the implications it might have when searching for dark‐sector physics. Use of supergravity equations in astronomy and late‐universe cosmology is often criticized on three grounds: (i) phenomenological success usually depends on the supergravity form for the scalar potential applying at the relevant energies; (ii) the low‐energy scalar potential is extremely sensitive to quantum effects involving very massive particles and so is rarely well‐approximated by classical calculations of its form; and (iii) almost all Standard Model particles count as massive for these purposes and none of these are supersymmetric. Why should Standard Model loops preserve the low‐energy supergravity form even if supersymmetry is valid at energies well above the electroweak scale? The authors use recently developed tools for coupling supergravity to non‐supersymmetric matter to estimate the loop effects of heavy non‐supersymmetric particles on the low‐energy effective action, and provide evidence that the supergravity form is stable against integrating out such particles (and so argues against the above objection). This suggests an intrinsically supersymmetric picture of Nature where supersymmetry survives to low energies within the gravity sector but not the visible sector (for which supersymmetry is instead non‐linearly realized). The authors then explore the couplings of both sectors in this picture and find that the presence of auxiliary fields in the gravity sector makes the visible sector share many features usually attributed to linearly realized supersymmetry although (unlike for the MSSM) a second Higgs doublet is not required for all Yukawa couplings to be non‐vanishing and changes the dimension of the operator generating the Higgs mass. A discussion follows about the naturalness of this picture and some of the implications it might have when searching for dark‐sector physics. [ABSTRACT FROM AUTHOR]

We provide evidence that slow roll is not possible in any parametrically controlled regime of the moduli space of string theory. This is proven in full generality in the asymptotic limit of the moduli space of type II and heterotic Calabi‐Yau compactifications for the dilaton and any number of Kähler moduli. Our results suggest that in order to build quintessence into string theory one must work in the interior of moduli space where numerical, even if not parametric, control could still be achieved. Evidence is provided that slow roll is not possible in any parametrically controlled regime of the moduli space of string theory. This is proven in full generality in the asymptotic limit of the moduli space of type II and heterotic Calabi‐Yau compactifications for the dilaton and any number of Kähler moduli. The results suggest that in order to build quintessence into string theory one must work in the interior of moduli space where numerical, even if not parametric, control could still be achieved. [ABSTRACT FROM AUTHOR]

Type IIB supergravity enjoys a discrete non‐Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F‐theory. Remarkably, a subtle modification of the standard 10d Chern‐Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green‐Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls. Type IIB supergravity enjoys a discrete non‐Abelian duality group, which has potential quantum anomalies. In this paper the authors explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, they find that they do not vanish, which naively would signal an inconsistency of F‐theory. Remarkably, a subtle modification of the standard 10d Chern‐Simons term cancels these anomalies, a fact which relies on the specific field content of type IIB supergravity. The authors also discover other ways to cancel this anomaly, via a topological analog of the Green‐Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls. [ABSTRACT FROM AUTHOR]

We construct supergravity models allowing to sequester the phenomenology of inflation from the Planckian energy scale physics. The procedure consists of two steps: At Step I we study supergravity models, which might be associated with string theory or M‐theory, and have supersymmetric Minkowski vacua with flat directions. At Step II we uplift these flat directions to inflationary plateau potentials. We find certain conditions which ensure that the superheavy fields involved in the stabilization of the Minkowski vacua at Step I are completely decoupled from the inflationary phenomenology. Here the construction of supergravity models is presented allowing to sequester the phenomenology of inflation from the Planckian energy scale physics. The procedure consists of two steps: At Step I supergravity models are studied, which might be associated with string theory or M‐theory, and have supersymmetric Minkowski vacua with flat directions. At Step II these flat directions will be uplifted to inflationary plateau potentials. One finds certain conditions which ensure that the superheavy fields involved in the stabilization of the Minkowski vacua at Step I are completely decoupled from the inflationary phenomenology. [ABSTRACT FROM AUTHOR]

We develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a T6Z2×Z2 orientifold with generalized fluxes and O3/O7‐planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theory to phenomenological inflationary plateau potentials: α‐attractors with 7 discrete values 3α=1,2,3,...,7. Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics. The authors develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a specific orientifold with generalized fluxes and O3/O7‐planes. At Step I, flux potentials are used which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II a nilpotent multiplet is added and the flat direction(s) of the type IIB string theory are uplifted to phenomenological inflationary plateau potentials: α ‐attractors with 7 discrete values 3α = 1, 2, 3,..., 7. Their cosmological predictions are determined by the hyperbolic geometry inherited from string theory. The masses of the heavy fields and the volume of the extra dimensions change during inflation, but this does not affect the inflationary dynamics. [ABSTRACT FROM AUTHOR]

We show that the BRST Lagrangian double copy construction of N=0 supergravity as the 'square' of Yang–Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double‐copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples. [ABSTRACT FROM AUTHOR]

Cosmological models of the early or late universe exhibit (quasi) de Sitter space‐times with different stability properties. Considering models derived from string theory, the swampland program does not provide for now a definite characterisation of this stability. In this work we focus on de Sitter solutions of 10d type II supergravities, candidates for classical de Sitter string backgrounds: surprisingly, all known examples are unstable with ηV<−1. We aim at proving the existence of such a systematic tachyon, and getting formally a bound on the value of ηV. To that end, we develop three methods, giving us various sufficient conditions for having a tachyon upon assumptions, in analogy with de Sitter no‐go theorems. Our analysis eventually indicates the existence of variety of different tachyons, and related bounds on ηV. We use this knowledge to find 10 new de Sitter solutions of type IIB supergravity, that have tachyons of a different kind, higher ηV values and new 6d geometries. One solution even appears to be stable, with however non‐compact extra dimensions. Cosmological models of the early or late universe exhibit (quasi) de Sitter space‐times with different stability properties. Considering models derived from string theory, the swampland program does not provide for now a definite characterisation of this stability. In this work the focus is set on de Sitter solutions of 10d type II supergravities, candidates for classical de Sitter string backgrounds: surprisingly, all known examples are unstable with ηv < −1. The aim is to prove the existence of such a systematic tachyon, and getting formally a bound on the value of ηv. To that end, three methods will be developed, giving various sufficient conditions for having a tachyon upon assumptions, in analogy with de Sitter no‐go theorems. The analysis eventually indicates the existence of variety of different tachyons, and related bounds on ηv. This knowledge is used to find 10 new de Sitter solutions of type IIB supergravity, that have tachyons of a different kind, higher ηv values and new 6d geometries. One solution even appears to be stable, with however non‐compact extra dimensions. [ABSTRACT FROM AUTHOR]

We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three‐dimensional Riemann‐Cartan space‐times. We use the language of exterior differential forms and the properties of Majorana spinors on 3‐dimensional space‐times to explicitly demonstrate the local supersymmetry of the action density involved. Exact coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion‐constraint imposed by the method of Lagrange multipliers. Cotton and Cottino 2‐forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated. The paper gives a discussion on the formulation of cosmological topologically massive (simple) supergravity theory in three‐dimensional Riemann‐Cartan space‐times. Using both the language of exterior differential forms and the properties of Majorana spinors on 3‐dimensional space‐times the authors explicitly demonstrate the local supersymmetry of the action density involved. Exact coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion‐constraint imposed by the method of Lagrange multipliers. Cotton and Cottino 2‐forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated. [ABSTRACT FROM AUTHOR]

We introduce the notion of G‐algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in En(n)×R+ exceptional generalised geometry for n∈{3,⋯,6}. Focusing on the exceptional case, we prove a classification of "exact" algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem. After discussing the general notion of Poisson–Lie duality, we show that the Poisson–Lie U‐duality is compatible with the equations of motion of supergravity. The authors introduce the notion of a G‐algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in En(n) × R+ exceptional generalised geometry for n ∈{3,...,6}. Focusing on the exceptional case, a classification of "exact" algebroids is proven and the related classification of Leibniz parallelisable spaces is translated into a tractable algebraic problem. After discussing the general notion of Poisson–Lie duality, it will be shown that the Poisson–Lie U‐duality is compatible with the equations of motion of supergravity. [ABSTRACT FROM AUTHOR]

We analyze to which extent the KKLT proposal for the construction of de Sitter vacua in string theory is quantitatively controlled. Our focus is on the quality of the 10d supergravity approximation. As our main finding, we uncover and quantify an issue which one may want to call the "singular‐bulk problem". In particular, we show that, requiring the curvature to be small in the conifold region, one is generically forced into a regime where the warp factor becomes negative in a significant part of the Calabi‐Yau orientifold. This implies true singularities, independent of the familiar, string‐theoretically controlled singularities of this type in the vicinity of O‐planes. We also discuss possible escape routes as well as other control issues, related to the need for a large tadpole and hence for a complicated topology. In this paper it is analyzed to which extent the KKLT proposal for the construction of de Sitter vacua in string theory is quantitatively controlled. The focus is on the quality of the 10d supergravity approximation. As main finding, the authors uncover and quantify an issue which one may want to call the "singular‐bulk problem". In particular, it is shown that, requiring the curvature to be small in the conifold region, one is generically forced into a regime where the warp factor becomes negative in a significant part of the Calabi‐Yau orientifold. This implies true singularities, independent of the familiar, string‐theoretically controlled singularities of this type in the vicinity of O‐planes. There is also a discussion about possible escape routes as well as other control issues, related to the need for a large tadpole and hence for a complicated topology. [ABSTRACT FROM AUTHOR]

We argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no‐scale supergravities in low‐energy 4D EFTs. We identify 4 nested types of no‐scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no‐scale properties (including non‐supersymmetric flat directions). We use these ideas to classify corrections to the low‐energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kähler potential at any fixed order in α′ and string loops agrees with all extant calculations. p‐form fields play two important roles: they spawn many (generalised) shift symmetries; and space‐filling 4‐forms teach 4D physics about higher‐dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models. In this paper it is argued that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and it is shown that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no‐scale supergravities in low‐energy 4D EFTs. The authors identify 4 nested types of no‐scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no‐scale properties (including nonsupersymmetric flat directions). These ideas are used to classify corrections to the low‐energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. The prediction derived for the Kähler potential at any fixed order in α′ and string loops agrees with all extant calculations. p‐form fields play two important roles: they spawn many (generalised) shift symmetries; and space‐filling 4‐forms teach 4D physics about higher‐dimensional phenomena like flux quantisation. The authors argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models. [ABSTRACT FROM AUTHOR]

We propose a generalisation of the Weak Gravity Conjecture in de Sitter space by studying charged black‐holes and comparing the gravitational and an abelian gauge forces. Using the same condition as in flat space, namely the absence of black‐hole remnants, one finds that for a given mass m there should be a state with a charge q bigger than a minimal value qmin(m,l), depending on the mass and the de Sitter radius l, in Planck units. In the large radius flat space limit (large l), qmin→m leading to the known result q>m/2, while in the highly curved case (small l) qmin behaves as ml. We also discuss the example of the gauged R‐symmetry in N=1 supergravity. The authors propose a generalisation of the Weak Gravity Conjecture in de Sitter space by studying charged black‐holes and comparing the gravitational and an abelian gauge forces. Using the same condition as in flat space, namely the absence of black‐hole remnants, one finds that for a given mass m there should be a state with a charge q bigger than a minimal value qmin(m,l), depending on the mass and the de Sitter radius l, in Planck units. In the large radius flat space limit (large l), qmin→m leading to the known result q>m/2, while in the highly curved case (small l) qmin behaves as ml. The example of the gauged R‐symmetry in N=1 supergravity is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six‐dimensional superconformal field theories and we believe that they also underlie potential future formulations of the (2,0)‐theory. We show that the connections on non‐abelian gerbes usually introduced in the literature are problematic in that they are locally gauge equivalent to connections on abelian gerbes. Connections on string structures form an exception and we introduce the general concept of an adjusted Weil algebra leading to potentially interacting connections on higher principal bundles. Considering a special case, we derive the metric extension of string structures and the corresponding adjusted Weil algebra. The latter lead to connections that were previously constructed by hand in the context of gauged supergravities. We also explain how the Leibniz algebras induced by an embedding tensor in gauged supergravities fit into our picture. In this paper, the mathematical formulation of metric string structures will be developed. These play a crucial role in the formulation of certain six‐dimensional superconformal field theories and one can asume that they also underlie potential future formulations of the (2,0)‐theory. The authors show that the connections on non‐abelian gerbes usually introduced in the literature are problematic in that they are locally gauge equivalent to connections on abelian gerbes. Connections on string structures form an exception and we introduce the general concept of an adjusted Weil algebra leading to potentially interacting connections on higher principal bundles. Considering a special case, the metric extension of string structures and the corresponding adjusted Weil algebra are derived. The latter lead to connections that were previously constructed by hand in the context of gauged supergravities. An explanation is given how the Leibniz algebras induced by an embedding tensor in gauged supergravities fit into this picture. [ABSTRACT FROM AUTHOR]

We construct AdS4 flux vacua of type IIA string theory in the supergravity (large volume, small gs) regime, including the backreaction of O6‐planes. Our solutions are the localized versions of the smeared solutions on Calabi‐Yau orientifolds studied by DeWolfe, Giryavets, Kachru and Taylor and in other works. We find that the O‐plane backreaction in these solutions generates warping, a varying dilaton, non‐closed RR field strengths and internal curvature. Just like their smeared counterparts, the localized solutions admit stabilized moduli, a parametric control over string corrections and a parametric separation between the AdS and KK scales. Our explicit expressions furthermore make precise the common lore that smeared solutions should approximate the exact ones in the large‐volume, small‐gs limit. Finally, our solutions appear to violate a recent swampland conjecture about an absence of scale separation in supersymmetric AdS vacua. We make a simple observation explaining why this happens in these solutions in contrast to most other AdS solutions in string theory. The author constructs AdS4 flux vacua of type IIA string theory in the supergravity (large volume, small gs) regime, including the backreaction of O6‐planes. The solutions are the localized versions of the smeared solutions on Calabi‐Yau orientifolds studied by DeWolfe, Giryavets, Kachru and Taylor and in other works. It is found that the O‐plane backreaction in these solutions generates warping, a varying dilaton, non‐closed RR field strengths and internal curvature. Just like their smeared counterparts, the localized solutions admit stabilized moduli, a parametric control over string corrections and a parametric separation between the AdS and KK scales. The explicit expressions furthermore make precise the common lore that smeared solutions should approximate the exact ones in the large‐volume, small‐gs limit. Finally, our solutions appear to violate a recent swampland conjecture about an absence of scale separation in supersymmetric AdS vacua. It follows a simple observation explaining why this happens in these solutions in contrast to most other AdS solutions in string theory. [ABSTRACT FROM AUTHOR]

Type IIB string theory on a 5‐sphere gives rise to N=8,SO(6) gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, we undertake an investigation of its critical points. The scalar manifold is an E6(6)/USp(8) coset, and the challenge is that it is 42‐dimensional. We take a Machine Learning approach to the problem using TensorFlow, and this results in a substantial increase in the number of known critical points. Our list of 32 critical points contains all five of the previously known ones, including an N=2 supersymmetric point identified by Khavaev, Pilch and Warner. Type IIB string theory on a 5‐sphere gives rise to N = 8, SO(6) gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, the authors undertake an investigation of its critical points. The scalar manifold is an E6(6) ∕ USp(8) coset, and the challenge is that it is 42‐dimensional. A Machine Learning approach to the problem using TensorFlow is chosen, and this results in a substantial increase in the number of known critical points. The obtained list of 32 critical points contains all five of the previously known ones, including an N = 2 supersymmetric point identified by Khavaev, Pilch and Warner. [ABSTRACT FROM AUTHOR]

We describe general classes of 6D and 4D F‐theory models with gauge group (SU(3)×SU(2)×U(1))/Z6. We prove that this set of constructions gives all possible consistent 6D supergravity theories with no tensor multiplets having this gauge group and the corresponding generic matter representations, which include those of the MSSM. We expect, though do not prove, that these models are similarly generic for 6D theories with tensor multiplets and for 4D N=1 supergravity theories. The largest class of these constructions come from deforming an underlying geometry with gauge symmetry SU(4)×SU(3)×SU(2). In this article general classes of 6D and 4D F‐theory models with gauge group (SU(3) X SU(2) X U(1))/ Z6 are described. For 6D F‐theory models with no tensor multiplets, the authors prove that this set of constructions gives all possible consistent supergravity theories with this gauge group and the corresponding generic matter representations, which include those of the MSSM. It is expected, though not proven, that these models are similarly generic for 6D theories with tensor multiplets and for 4D N = 1 supergravity theories. The models in the largest class of these constructions come from deforming an underlying geometry with gauge group SU(4) XSU(3) X SU(2), corresponding to Higgsing on three bifundamental fields. [ABSTRACT FROM AUTHOR]

We study warped AdS3 solutions in massive IIA supergravity preserving N=(3,0) and N=(1,0) supersymmetry. We consider solutions whose internal spaces decompose as an S3 × S3 fibration and a interval over which the rest of the solution is foliated. We present necessary and sufficient conditions for these solutions to exist, in terms of systems of ordinary differential equations and find several new analytic and numerical examples with internal spaces bounded between D‐brane and O‐plane behaviors. The authors study warped AdS3 solutions in massive IIA supergravity preserving N = (3; 0) and N = (1; 0) supersymmetry. They consider solutions whose internal spaces decompose as an S3 × S3 fibration and an interval over which the rest of the solution is foliated. Necessary and sufficient conditions for these solutions are presented in terms of systems of ordinary differential equations. Several new analytic and numerical examples with internal spaces bounded between D‐brane and O‐plane behaviors are found. [ABSTRACT FROM AUTHOR]

We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to infinite left braces are given. Indecomposable solutions of the Yang–Baxter equation are explored using the structure of skew left braces. [ABSTRACT FROM AUTHOR]

We discuss the physical applications of supergravity to the dark side of our universe, comprising cosmological inflation, dark energy, and dark matter (DM). Supergravity is the meeting point of cosmology, gravity, and high‐energy physics of elementary particles, which makes it the natural framework to unify fundamental interactions and fundamental scales under Planck scale. In order to make our presentation accessible to a larger audience, we skip all technical details about supergravity theory and concentrate on the conceptual issues of supergravity applications to cosmology. We conjecture the gravitational origin of the cosmological inflation (in the modified gravity), the dark energy (as the positive cosmological constant), and the DM (made of gravitino particles) in supergravity. [ABSTRACT FROM AUTHOR]

Abstract: Among the possible superalgebras that contain the AdS3 isometries, two interesting possibilities are the exceptional F(4) and G(3). Their R‐symmetry is respectively SO(7) and G2, and the amount of supersymmetry N = 8 and N = 7. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six‐sphere fibred over an interval, with an O8‐plane at one end. The R‐symmetry is the symmetry group of the sphere; in the G(3) case, it is broken to G2 by fluxes. We also find several numerical N = 1 solutions with G2 flavor symmetry, with various localized sources, including O2‐planes and O8‐planes. [ABSTRACT FROM AUTHOR]

Abstract: The UV finiteness found in calculations of the 4‐point amplitude in N = 5 supergravity at loop order L = 3 , 4 has not been explained, which motivates our study of the relevant superspace invariants and on‐shell superamplitudes for both N = 5 and N = 6. The local 4‐point superinvariants for L = 3 , 4 are expected to have nonlinear completions whose 6‐point amplitudes have non‐vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For N = 5, we find at L = 3 that local 6‐point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4‐point counterterm and thus gives a plausible explanation of the observed L = 3 finiteness. However, at L = 4 we construct a local 6‐point superinvariant with non‐vanishing SSL's, so the SSL argument does not explain the observed L = 4 N = 5 UV finiteness. For N = 6 supergravity there are no 6‐point invariants at either L = 3 or 4, so the SSL argument predicts UV finiteness. [ABSTRACT FROM AUTHOR]

Abstract: We discuss local supercurrents as sources of the super‐Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet–Iliopoulos term. Curvature multiplets can be used as alternative to the gravitino variation in the search for rigid supersymmetric curved backgrounds. [ABSTRACT FROM AUTHOR]

Abstract: We use F‐theory to study gauge algebra preserving transitions of 6d supergravity theories that are connected by superconformal points. While the vector multiplets remain unchanged, the hyper‐ and tensor multiplet sectors are modified. In 6d F‐theory models, these transitions are realized by tuning the intersection points of two curves, one of them carrying a non‐Abelian gauge algebra, to a (4,6,12) singularity, followed by a resolution in the base. The six‐dimensional supergravity anomaly constraints are strong enough to completely fix the possible non‐Abelian representations and to restrict the Abelian charges in the hypermultiplet sector affected by the transition, as we demonstrate for all Lie algebras and their representations. Furthermore, we present several examples of such transitions in torically resolved fibrations. In these smooth models, superconformal points lead to non‐flat fibers which correspond to non‐toric Kähler deformations of the torus‐fibered Calabi‐Yau 3‐fold geometry. [ABSTRACT FROM AUTHOR]

We study the constraints of spacetime supersymmetry for perturbative three- and two-dimensional Minkowski vacua of the critical heterotic string. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, we describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions we show that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification. As a recent orbifold construction shows, in two dimensions there are more exotic possibilities, and we discuss how these fit into our analysis. [ABSTRACT FROM AUTHOR]

Abstract: We review the group‐geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of d = 3 , 4 off‐shell supergravities and d = 5 Chern‐Simons supergravity are discussed in detail. A cursory account of d = 10 + 2 supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians d‐forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in d = s + t dimensions are summarized in Appendices. [ABSTRACT FROM AUTHOR]

Abstract: We classify N = 2 Minkowski4 solutions of IIB supergravity with an S U ( 2 ) R symmetry geometrically realized by an S2‐foliation in the remaining six dimensions. For the various cases of the classification, we reduce the supersymmetric system of equations to PDEs. These cases often accommodate systems of intersecting branes and half‐maximally supersymmetric AdS5, 6, 7 solutions when they exist. As an example, we analyze the AdS6 case in more detail, reducing the supersymmetry equations to a single cylindrical Laplace equation. We also recover an already known linear dilaton background dual to the (1, 1) Little String Theory (LST) living on NS5‐branes, and we find a new Minkowski5 linear dilaton solution from brane intersections. Finally, we also discuss some simple Minkowski4 solutions based on compact conformal Calabi‐Yau manifolds. [ABSTRACT FROM AUTHOR]

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. [ABSTRACT FROM AUTHOR]

We focus on non-linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss-Bonnet multiplet and discuss the emergence of a new scalar degree of freedom. [ABSTRACT FROM AUTHOR]

We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a 'generalised parallelisation' with a frame algebra with constant coefficients. The consistent truncation then arises as a generalised version of a conventional Scherk-Schwarz reduction with the frame algebra encoding the embedding tensor of the reduced theory. The key new result is that all round-sphere [ABSTRACT FROM AUTHOR]

We discuss the possible realisation in string/M theory of the recently discovered family of four-dimensional maximal [ABSTRACT FROM AUTHOR]

We study [ABSTRACT FROM AUTHOR]

The complete classification of the nilpotent orbits of SO(2,2)2 in the representation (2,2,2,2), achieved in , is applied to the study of multi-center, asymptotically flat, extremal black hole solutions to the STU model. These real orbits provide an intrinsic characterization of regular single-center solutions, which is invariant with respect to the action of the global symmetry group SO(4,4), underlying the stationary solutions of the model, and provide stringent regularity constraints on multi-centered solutions. The known almost-BPS and composite non-BPS solutions are revisited in this setting. We systematically provide, for the relevant SO(2,2)2-nilpotent orbits of the global Noether charge matrix, regular representatives thereof. This analysis unveils a composition law of the orbits according to which those containing regular multi-centered solutions can be obtained as combinations of specific single-center orbits defining the constituent black holes. Some of the SO(2,2)2-orbits of the total Noether charge matrix are characterized as 'intrinsically singular' in that they cannot contain any regular solution. [ABSTRACT FROM AUTHOR]

In the study of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determine the nilpotent orbits of a real symmetric pair. We apply our methods to an explicit example, and thereby classify the nilpotent orbits of [ABSTRACT FROM AUTHOR]

In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0 S-resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras. This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras. We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature. [ABSTRACT FROM AUTHOR]

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrödinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large-scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set-up might provide an interesting new arena for testing the ideas of holography and gravitational duals. [ABSTRACT FROM AUTHOR]

We derive the mass formulae for [ABSTRACT FROM AUTHOR]

We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the [ABSTRACT FROM AUTHOR]