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In light of NANOGrav data, we provide for the first time possible observational signatures of Superstring theory. First, we work with inflection-point inflationary potentials naturally realized within Wess–Zumino-type no-scale Supergravity, which give rise to the formation of microscopic primordial black holes (PBHs) triggering an early matter-dominated era (eMD) and evaporating before big bang nucleosynthesis (BBN). Remarkably, we obtain an abundant production of primordial gravitational waves (PGW) at the frequency ranges of nHz, Hz and kHz and in strong agreement with pulsar time array (PTA) gravitational wave (GW) data. This PGW background could serve as a compelling observational signature for the presence of quantum gravity via no-scale Supergravity. [ABSTRACT FROM AUTHOR]

It has been shown recently that superstring states are organized into supermultiplets for the massless fundamental modes and solitons representing excited states. Summation of superstring amplitudes yields an expression that has poles when the momenta of the external states have specific values. It is established that only the residues and not the mass can be shifted by higher genus terms in the superstring perturbation series. The masses of elementary particles will not be generated by radiative corrections in superstring theory. Quantization of the energy levels does occur for the excited modes and the solitons. The superstring must be replaced by a hadronic string to achieve a phenomenologically viable theory of the particle spectrum. A linear spacing for the masses can be derived from the pion bubble model. The vibrational modes of the string between the quark and anti-quark in the pion then generates square-root variations from the integer multiple rule for the excited states of hadrons. [ABSTRACT FROM AUTHOR]

We consider a low-energy effective theory of p -branequaes in a D -dimensional spacetime, and impose two conditions: (1) the theory is scale-invariant, and (2) the electric–magnetic dual |$(D-p-4)$| -branes exist and they obey the same type of interactions to the p -branes. (We also assume other natural conditions such as Lorentz invariance but not string theory, supersymmetry, supergravity, and so on.) We then ask what values of p and D are consistent with these conditions. Using simple dimensional analysis, we find that only two solutions are possible: |$(p,D)=(2,11)$| and |$(p,D)=(2n-1,4n+2)$|⁠ , (⁠|$n=1,2,3,\cdots$|⁠). The first solution corresponds to M-theory, and the second solutions at |$n=1$| and |$n=2$| correspond to self-dual strings in little string theory and D3-branes in type IIB superstring theory, respectively, while the second solutions for |$n \ge 3$| are unknown but would be higher spin theories. Thus, quantum gravity (massless spin two theory) satisfying our two conditions would only be superstring theories, and the conditions would be strong enough to characterize superstring theories in quantum gravity. [ABSTRACT FROM AUTHOR]

We propose a covariant method of constructing entire trajectories of physical states in superstring theory in the critical dimension. It is inspired by a recently developed covariant technology of excavating bosonic string trajectories, that is facilitated by the observation that the Virasoro constraints can be written as linear combinations of lowering operators of a bigger algebra, namely a symplectic algebra, which is Howe dual to the spacetime Lorentz algebra. For superstrings, it is the orthosymplectic algebra that appears instead, with its lowest weight states forming the simplest class of physical trajectories in the NS sector. To construct the simplest class in the R sector, the lowest weight states need to be supplemented with other states, which we determine. Deeper trajectories are then constructed by acting with suitable combinations of the raising operators of the orthosymplectic algebra, which we illustrate with several examples. [ABSTRACT FROM AUTHOR]

Aspects of superstring theory on deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace T T ¯ holography, are presented. The excitation energy of a singly wound long string plus its contribution to the energy of the black hole, 1/p fraction of the black-hole energy, is the same as that in T T ¯ deformed CFT2 with c = 6k. This supports the claim that the black hole can be thought of as a state in a symmetric product of p CFT2's of central charge 6k, where the black-hole energy is split equally among all p factors. A comment on superstring theory on deformed global AdS3 is also presented. [ABSTRACT FROM AUTHOR]

Carrollian holography is supposed to describe gravity in four-dimensional asymptotically flat space-time by the three-dimensional Carrollian CFT living at null infinity. We transform superstring scattering amplitudes into the correlation functions of primary fields of Carrollian CFT depending on the three-dimensional coordinates of the celestial sphere and a retarded time coordinate. The power series in the inverse string tension is converted to a whole tower of both UV and IR finite descendants of the underlying field-theoretical Carrollian amplitude. We focus on four-point amplitudes involving gauge bosons and gravitons in type I open superstring theory and in closed heterotic superstring theory at the tree-level. We also discuss the limit of infinite retarded time coordinates, where the string world-sheet becomes celestial. [ABSTRACT FROM AUTHOR]

In this study, we thoroughly investigate the covariant and B-field gauge invariant odd-parity NS-NS couplings at order α ′ 3 , while considering the removal of field redefinitions, Bianchi identities, and total derivative freedoms. Our comprehensive analysis reveals the existence of 477 independent couplings. To establish a specific basis, we construct it in such a way that none of the couplings contain terms involving structures such as R, R μ ν , ∇ μ H μ α β , ∇ μ ∇ μ Φ , or terms with more than two derivatives, except for one term that possesses three derivatives on H. Interestingly, the mentioned coupling with the four-derivative on the B-field is rendered zero by the sphere-level three-point S-matrix element. Furthermore, we demonstrate that the remaining 476 parameters in type II superstring theory are fixed to zero by imposing the requirement that the circular reduction of the couplings remains invariant under O (1 , 1 , Z) T-duality transformations. This result is consistent with our expectations and highlights the crucial role played by the O (1 , 1 , Z) symmetry in constraining the parameter space of the classical effective actions in string theory. [ABSTRACT FROM AUTHOR]

In the sixties, A. Gray [19] and B. O'Neill [27] come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories. [ABSTRACT FROM AUTHOR]

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups S O (3 2) and E 8 × E 8 . The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin- 1 2 fields transform under the adjoint representation in these models, compactification of the heterotic string over G 2 / S U (3) or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over G 2 × S U (2) × U (1) S U (3) × U (1) ′ × U (1) ′ ′ , provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin- 1 2 fields now would transform under the fundamental representation of G 2 × S U (2) × U (1) and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the G 2 × S U (2) × U (1) model vanishes at n 1 2 ≃ 1 0 3. 3 4 2 7 1 9 2 4. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions. [ABSTRACT FROM AUTHOR]

The type IIB matrix model, also known as the IKKT model, has been proposed as a promising candidate for a non-perturbative formulation of superstring theory. Based on this proposal, various attempts have been made to explain how our four-dimensional space-time can emerge dynamically from superstring theory. In this article, we review the progress in numerical studies on the type IIB matrix model. We particularly focus on the most recent results for the Euclidean and Lorentzian versions, which are obtained using the complex Langevin method to overcome the sign problem. We also review the earlier results obtained using conventional Monte Carlo methods and clarify the relationship among different calculations. [ABSTRACT FROM AUTHOR]

We discuss a decomposition formula of simple products of fermion correlation functions with cyclic constrains and its applications to spin sums of super string amplitudes.Based on some facts which are noted or derived in this paper, we propose a candidate of the form of this decomposition formula for some of higher genus cases which includes genus 2 case. Although we had to use several conjectures and assumptions due to unsolved mathematical difficulties, the method described in the text may be an efficient way to obtain the decomposition formula in some of higher genus cases. In particular, for those cases, we propose a concrete method to sum over non-singular even spin structures for the product of arbitrary number of the fermion correlation functions with cyclic constraints in super string amplitudes.We also propose an explicit generalization of Eisenstein-Kronecker series to the higher genus cases in the process of considerations above.

Ten-dimensional Superstring theory unifies the Standard Model of the strong, electromagnetic, and weak interactions with quantum gravity. Starting with 10-dimensional superstring theory, we can get a 4-dimensional theory with spacetime supersymmetry following the Kaluza–Klein idea by compactifying six of the ten dimensions. For phenomenological reasons we need to do this while maintaining Supersymmetry of 4-dimensional spacetime. To achieve this, as Candelas, Horowitz, Strominger, and Witten [1] have shown, we must compactify six of the ten dimensions of to the so called Calabi–Yau manifolds. Another equivalent approach developed by D. Gepner [2, 3] is the compactification of 6 dimensions onto some Superconformal Field theory with the central charge . Each of these two equivalent approaches has its own merits. Say, using exactly solvability of the Minimal models of Superconformal Field Theory, it is possible to obtain the explicit solution of the considered models. In this article we review a series of our works on Calabi–Yau manifolds, their mirror symmetry, special geometry on the moduli space of Calabi–Yau, the connection of Calabi–Yau manifolds with superconformal minimal models and with supersymmetric gauged linear sigma models. [ABSTRACT FROM AUTHOR]

Matrix theory is a proposed non-perturbative definition of superstring theory in which space is emergent. Recently, it was shown that space-time can emerge with a scale-invariant spectrum of cosmological perturbations which is sourced by thermal fluctuations of the BFSS model at finite temperature. Inspired by these results, we begin a study of the IKKT model at finite temperature. We find that in this model, which is closely related to the BFSS model at finite temperature, thermal fluctuations can also source a scale-invariant spectrum of scalar and tensor fluctuations. [ABSTRACT FROM AUTHOR]

The duality between type IIA superstring theory and M-theory enables us to lift bound states of D0-branes and n parallel D6-branes to M-theory compactified on an n-centered multi-Taub-NUT space TN n. Accordingly, the rank n K-theoretic Donaldson-Thomas invariants of ℂ3 are connected with the index of M-theory on ℂ3 × TN n. In this paper, we extend this connection by considering intersecting D6-branes. In the presence of a suitable Neveu-Schwarz B-field, the system preserves two supercharges. This system is T-dual to the configuration of tetrahedron instantons which we introduced in [1]. We conjecture a closed-form expression for the K-theoretic tetrahedron instanton partition function, which is the generating function of the D0-D6 partition functions. We find that the tetrahedron instanton partition function coincides with the partition function of the magnificent four model for special values of the parameters, leading us to conjecture that our system of intersecting D6-branes can be obtained from the annihilation of D8-branes and anti-D8-branes. Remarkably, the K-theoretic tetrahedron instanton partition function allows an interpretation in terms of the index of M-theory on a noncompact Calabi-Yau fivefold which is related to a superposition of Kaluza-Klein monopoles. The dimensional reduction of the system allows us to express the cohomological tetrahedron instanton partition function in terms of the MacMahon function, generalizing the correspondence between Gromov-Witten invariants and Donaldson-Thomas invariants for Calabi-Yau threefolds. [ABSTRACT FROM AUTHOR]

We study a decoupling limit of M-theory where the three-form gauge potential becomes critical. This limit leads to nonrelativistic M-theory coupled to a non-Lorentzian spacetime geometry. Nonrelativistic M-theory is U-dual to M-theory in the discrete light cone quantization, a non-perturbative approach related to the Matrix theory description of M-theory. We focus on the compactification of nonrelativistic M-theory over a two-torus that exhibits anisotropic behaviors due to the foliation structure of the spacetime geometry. We develop a frame covariant formalism of the toroidal geometry, which provides a geometrical interpretation of the recently discovered polynomial realization of SL(2 , ℤ) duality in nonrelativistic type IIB superstring theory. We will show that the nonrelativistic IIB string background fields transform as polynomials of an effective Galilean "boost velocity" on the two-torus. As an application, we construct an action principle describing a single M5-brane in nonrelativistic M-theory and study its compactification over the anisotropic two-torus. This procedure leads to a D3-brane action in nonrelativistic IIB string theory that makes the SL(2 , ℤ) invariance manifest in the polynomial realization. [ABSTRACT FROM AUTHOR]

The superconformal algebra characters have to exhibit modular invariance in order to be appropriately applied in quantum superstring theories. The nonunitary characters are given by higher-level Appell functions and different kinds of Jacobi theta functions are involved within their algebraic structures. Evaluating their -modular invariance appears to be quite simple, but verifying their -modular invariance entails a serious mathematical physics exploration. In this regard, we use a new vocabulary for Jacobi theta functions, namely "spectral theta functions," which allows us to come up with the -modular transformation of nonunitary (nontrivial) characters for the central charge , where is a pair of coprime positive integers. [ABSTRACT FROM AUTHOR]

We review a cosmological model where the metric determinant plays a dynamical role and present new numerical results on the cancellation of the vacuum energy density including the contribution of a cosmological constant. The action of this model is only invariant under restricted coordinate transformations with unit Jacobian (the same restriction appears in the well-known unimodular-gravity approach to the cosmological constant problem). As to the possible origin of the nonstandard terms in the matter action of the model, we show that these terms can, in principle, arise from the emergent gravity in the IIB matrix model, a nonperturbative formulation of superstring theory. [ABSTRACT FROM AUTHOR]

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient α, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although α has a unique value in M-theory, we found no evidence of an upper bound on α in 11D. [ABSTRACT FROM AUTHOR]

Using the ambitwistor string theory, we study graviton scattering amplitudes in a light-like linear dilaton background of 10-dimensional supergravity. At the tree level, we find that the three-graviton amplitude coincides with the type-II superstring theory, and the four-graviton or more amplitudes differ from the superstring theory but satisfy the scattering equations. Due to a modified momentum conservation law different at each order in genus expansion, a nonzero amplitude is determined solely from the particular order in perturbation theory without further corrections. [ABSTRACT FROM AUTHOR]

The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szegö kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the two-point function. The hyper-elliptic formulation of genus-two Riemann surfaces is used to derive these results, and its SL(2, ℂ) covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann ϑ-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers. [ABSTRACT FROM AUTHOR]

We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour. [ABSTRACT FROM AUTHOR]

We investigate effects of fermionic T‐duality on type II superstring in presence of Ramond‐Ramond (RR) field that has infinitesimal linear dependence on bosonic coordinate xμ. Other fields are assumed to be constant. Procedure that we employ for obtaining fermionic T‐dual theory is Buscher procedure, where we will consider two distinct cases. One, where action has not been T‐dualized along bosonic coordinates and other where it has. By analyzing these two cases, their actions and T‐dual transformation laws, we obtain some insight into how background fields transform and what are necessary ingredients for emergence of fermionic non‐commutativity. The authors investigate effects of fermionic T‐duality on type II superstring in presence of Ramond‐Ramond (RR) field that has infinitesimal linear dependence on bosonic coordinate xμ. Other fields are assumed to be constant. The employed procedure for obtaining fermionic T‐dual theory is Buscher procedure with consideration of two distinct cases. One, where action has been T‐dualized along bosonic coordinates and the other where it has not. By analyzing these two cases, their actions and T‐dual transformation laws, one obtains some insight into how background fields transform and what are necessary ingredients for emergence of fermionic non‐commutativity. [ABSTRACT FROM AUTHOR]

We propose a new splitting behavior of tree-level string/particle amplitudes for massless scalars, gluons and gravitons. We identify certain subspaces in the space of Mandelstam variables, where the universal Koba-Nielsen factor splits into two parts (each with an off-shell leg). Both open- and closed-string amplitudes with Parke-Taylor factors naturally factorize into two stringy currents , which implies the splitting of bi-adjoint ϕ 3 amplitudes and via a simple deformation to unified stringy amplitudes, the splitting of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory; the same splitting holds for scalar amplitudes without color such as the special Galileon. Remarkably, if we impose similar constraints on Lorentz products involving polarizations, gluon and graviton amplitudes in bosonic string and superstring theories also split into two (stringy) currents. A special case of the splitting implies soft theorems, and more generally it extends recently proposed smooth splittings and new factorizations near zeros to all these theories. [ABSTRACT FROM AUTHOR]

This article reviews some results of the SAGEX programme that have developed in the understanding of the interplay of supersymmetry and modular covariance of scattering amplitudes in type IIB superstring theory and its holographic image in N = 4 supersymmetric Yang–Mills theory (SYM). The first section includes the determination of exact expressions for BPS interactions in the low-energy expansion of type IIB superstring amplitudes. The second section concerns properties of a certain class of integrated correlators in N = 4 SYM with arbitrary classical gauge group that are exactly determined by supersymmetric localisation. Not only do these reproduce known features of perturbative and non-perturbative N = 4 SYM for any classical gauge group, but they have large- N expansions that are in accord with expectations based on the holographic correspondence with superstring theory. The final section focusses on modular graph functions. These are modular functions that are closely associated with coefficients in the low-energy expansion of superstring perturbation theory and have recently received quite a lot of interest in both the physics and mathematics literature. [ABSTRACT FROM AUTHOR]

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments. [ABSTRACT FROM AUTHOR]

Superstring theories in ten dimensions allow spacetime supersymmetry breaking at the string scale at the expense of controlled Minkowski backgrounds. The next-to-maximally symmetric backgrounds, found by Dudas and Mourad, involve a warped compactification on an interval associated with codimension-one defects. We generalize these solutions by varying the effective field theory parameters, and we discuss the dimensional reduction on the interval. In particular, we show that scalars and form fields decouple in a certain range of dimensions, yielding Einstein-Yang-Mills theory. Moreover, we find that the breakdown of this effective description due to light Kaluza-Klein modes reflects the swampland distance conjecture, supporting the consistency of the picture at least qualitatively. [ABSTRACT FROM AUTHOR]

Open superstring field theory admits a "hybrid" formulation where N = 1 D = 4 supersymmetry is manifest for Calabi-Yau compactifications to four dimensions. Using this formulation, the half-BPS instanton solution of four-dimensional super-Yang-Mills can be easily generalized to the full open superstring field theory. In this paper, we compute the first stringy correction to the super-Yang-Mills instanton solution which involves turning on certain fields at the first massive level. [ABSTRACT FROM AUTHOR]

We construct open-closed superstring interactions based on the open-closed homotopy algebra structure. This provides a classical open superstring field theory on general closed-superstring-field backgrounds described by classical solutions of the nonlinear equation of motion of the closed superstring field theory. We also give the corresponding WZW-like action through the map connecting the homotopy-based and WZW-like formulations. [ABSTRACT FROM AUTHOR]

Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations to the applicability of effective field theory techniques in describing early Universe cosmology. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'. [ABSTRACT FROM AUTHOR]

We interpret the lack of large-angle temperature correlations and the even-odd parity imbalance observed in the cosmic microwave background (CMB) by COBE, WMAP and Planck satellite missions as a possible stringy signal ultimately stemming from a composite inflaton field (e.g., a fermionic condensate). Based on causality arguments and a Fourier analysis of the angular two-point correlation function, two infrared cutoffs k min even , odd (satisfying k min even ≃ 2 k min odd ) are introduced to the CMB power spectrum associated, respectively, with periodic and antiperiodic boundary conditions of the fermionic constituents (echoing the Neveu–Schwarz–Ramond model in superstring theory), without resorting to any particular model. [ABSTRACT FROM AUTHOR]

We describe how to calculate the Hagedorn temperature of N = 4 SYM theory and type IIB superstring theory on AdS5 × S5 via the Quantum Spectral Curve (QSC) — providing further details on our previous letters [1] and [2]. We solve the QSC equations perturbatively at weak 't Hooft coupling λ up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of N = 4 SYM theory (real-β and γi deformation) agrees with the one in N = 4 SYM theory at any value of λ. [ABSTRACT FROM AUTHOR]

The leading (α ′) 3 -correction to the gravitational low-energy effective action of closed (type II) superstring theory in four-spacetime dimensions defines the Einstein-Grisaru-Zanon gravity action that is applied for a calculation of the leading corrections to the Schwarzschild solution and the Hubble function in the Friedmann-Lemaitre-Robertson-Walker universe, in the first order with respect to the effective string-generated coupling. The solutions found are compared to the corresponding solutions in the Einstein-Bel-Robinson gravity that also modifies the Einstein gravity by the terms quartic in the spacetime curvature. We consider the black hole shadows in the Einstein-Grisaru-Zanon gravity theory and derive the upper bound on the string coupling parameter from the Hawking temperature of a black hole. [ABSTRACT FROM AUTHOR]

It was shown by Kirzhnits and Chechen, following an earlier paper by Mead, that the minimum length scale l is constrained by the Mössbauer effect, which leads to the result cm, assuming the Snyder discrete space–time and conventional nuclides. Here, we note, firstly, that some recently discussed nuclides, for example , have much narrower natural line widths, which, if excited by synchrotron radiation, could potentially decrease the limiting value to cm in future experiments. The Snyder space–time and the superstring theory are both locally Lorentz invariant, and give rise to the same form of generalized indeterminacy principle, if we set , where is the Regge slope parameter, which is thus also constrained by the Mössbauer effect. For the heterotic superstring, in particular, cm, apparently beyond experimental reach. A hadron string theory at energy ~250 MeV, however, would be ruled out, since then cm. We emphasize that these results all presuppose a de Sitter momentum space, for the alternative anti-de Sitter momentum space implies no minimum length scale, and therefore seems unphysical. [ABSTRACT FROM AUTHOR]

We study the confinement/deconfinement transition in the D0-brane matrix model (often called the BFSS matrix model) and its one-parameter deformation (the BMN matrix model) numerically by lattice Monte Carlo simulations. Our results confirm general expectations from the dual string/M-theory picture for strong coupling. In particular, we observe the confined phase in the BFSS matrix model, which is a nontrivial consequence of the M-theory picture. We suggest that these models provide us with an ideal framework to study the Schwarzschild black hole, M-theory, and furthermore, the parameter region of the phase transition between type IIA superstring theory and M-theory. A detailed study of M-theory via lattice Monte Carlo simulations of the D0-brane matrix model might be doable with much smaller computational resources than previously expected. [ABSTRACT FROM AUTHOR]

We show that the massless integrable sector of the AdS 3 × S 3 × T 4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact minimal solutions to the form factor axioms, in integral form, based on analyticity considerations, along the same lines of ordinary relativistic integrable models. We construct in full detail the formulas for the two- and three-particle case, and show the similarities as well as the differences with respect to the off-shell Bethe ansatz procedure of Babujian et al. We show that our expressions pass a series of non-trivial consistency checks which are substantially more involved than in the traditional case. We speculate on the problems concerned in a possible generalisation to an arbitrary number of particles, and on a possible connection with the hexagon programme. [ABSTRACT FROM AUTHOR]

We review warped compactifications of superstring theory with some attention to the limit in which these resemble "bottom-up" phenomenological models. In addition to some discussion of the original Klebanov–Witten and Klebanov–Strassler setups, we also touch on various generalizations of the geometry that have been considered. Various other systems with a holographic duality are also briefly reviewed. The point of this latter exploration is to illustrate how far beyond the standard AdS5 × S5 setup things have moved over the years. [ABSTRACT FROM AUTHOR]

We show that the massless integrable sector of the AdS 3 × S 3 × T 4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact minimal solutions to the form factor axioms, in integral form, based on analyticity considerations, along the same lines of ordinary relativistic integrable models. We construct in full detail the formulas for the two- and three-particle case, and show the similarities as well as the differences with respect to the off-shell Bethe ansatz procedure of Babujian et al. We show that our expressions pass a series of non-trivial consistency checks which are substantially more involved than in the traditional case. We speculate on the problems concerned in a possible generalisation to an arbitrary number of particles, and on a possible connection with the hexagon programme. [ABSTRACT FROM AUTHOR]

We consider the gauge/gravity correspondence between maximally supersymmetric Yang–Mills theory in (p + 1) dimensions and superstring theory on the near-horizon limit of the D p -brane solution. The string-frame metric is AdS p + 2 × S 8 − p times a Weyl factor, and there is no conformal symmetry except for p = 3. In a previous paper by one of the present authors, the free-field result of gauge theory has been reproduced from string theory for a particular operator that has angular momentum along S 8 − p . In this paper, we extend this result to operators that have angular momenta along AdS p + 2. Our approach is based on a Euclidean formulation proposed by Dobashi et al. [Nucl. Phys. B 665 , 94 (2003)] and on the "string bit" picture. We first show that the spinning string solution in Lorentzian AdS, found by Gubser et al. [Nucl. Phys. B 636 , 99 (2002)], can be recast in a form that connects two points on the boundary of Euclidean AdS. The transition amplitudes of such strings can be interpreted as gauge theory correlators. We study the case of zero gauge coupling by ignoring interactions among string bits (massless particles in 10D spacetime that constitute a string), and show that the free-field results of gauge theory are reproduced. [ABSTRACT FROM AUTHOR]

We summarize recent results regarding single and double soft theorems of two different particles named dilatons, the Nambu-Goldstone boson of the spontaneously broken conformal field theories and the massless scalar particle of the closed string theories. Similarities and differences between the soft theorems of these two particles are discussed as well as their connections with the symmetries of the theories. [ABSTRACT FROM AUTHOR]

In this paper, the open string is quantized in a time-dependent black hole background. By time-dependent black hole, one means a Vaydia geometry in the adiabatic approximation, which in 2 + 1 dimensions is a BTZ black hole with a time-dependent mass. The worldsheet two-point function is derived and it is shown to have the same type of singularity as the flat space one. However, the equal times two-point function depends on the particular Cauchy surface where the worldsheet fields are defined. Finite temperature effects are incorporated through the Liouville–von Neumann approach to nonequilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded in partial waves with all positive coefficients. While this follows (rather indirectly) from the no-ghost theorem, the simplicity of the statement and its fundamental importance for the physical consistency of string theory begs for a more direct and elementary understanding. In this note we take a step in this direction by presenting a new expression for the partial wave coefficients of string amplitudes, given by surprisingly simple double/triple contour integrals for open/closed strings. This representation allows us to directly prove unitarity of all superstring theories in D ≤ 6 spacetime dimensions, and can also be used to determine various asymptotics of the partial waves at large mass levels. [ABSTRACT FROM AUTHOR]

Modular graph functions (MGFs) are SL(2, ℤ)-invariant functions on the Poincaré upper half-plane associated with Feynman graphs of a conformal scalar field on a torus. The low-energy expansion of genus-one superstring amplitudes involves suitably regularized integrals of MGFs over the fundamental domain for SL(2, ℤ). In earlier work, these integrals were evaluated for all MGFs up to two loops and for higher loops up to weight six. These results led to the conjectured uniform transcendentality of the genus-one four-graviton amplitude in Type II superstring theory. In this paper, we explicitly evaluate the integrals of several infinite families of three-loop MGFs and investigate their transcendental structure. Up to weight seven, the structure of the integral of each individual MGF is consistent with the uniform transcendentality of string amplitudes. Starting at weight eight, the transcendental weights obtained for the integrals of individual MGFs are no longer consistent with the uniform transcendentality of string amplitudes. However, in all the cases we examine, the violations of uniform transcendentality take on a special form given by the integrals of triple products of non-holomorphic Eisenstein series. If Type II superstring amplitudes do exhibit uniform transcendentality, then the special combinations of MGFs which enter the amplitudes must be such that these integrals of triple products of Eisenstein series precisely cancel one another. Whether this indeed is the case poses a novel challenge to the conjectured uniform transcendentality of genus-one string amplitudes. [ABSTRACT FROM AUTHOR]

In this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB‐exact exceptional algebroid (corresponding to the group En(n)×R+$\mathsf {E}_{n(n)}\times \mathbb {R}^+$, for n≤6$n\le 6$) locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat gl(2,R)$\mathfrak {gl}(2,\mathbb {R})$‐connection, a covariantly closed pair of 3‐forms, and a 5‐form, and comment on their physical interpretation. Using this analysis we reduce the search for Leibniz parallelisable spaces, and hence maximally supersymmetric consistent truncations, to a simple algebraic problem. We show that the exceptional algebroid perspective also gives a simple description of Poisson–Lie U‐duality without spectators and hence of generalised Yang–Baxter deformations. In this note the authors study exceptional algebroids, focusing on their relation to type IIB superstring theory. It is shown that a IIB‐exact exceptional algebroid (corresponding to the group En(n) × R+, for n ≤ 6) locally has a standard form given by the exceptional tangent bundle. Possible twists, a covariantly closed pair of 3‐forms, and a 5‐form are derived and commented on their physical interpretation. Using this analysis, the search for Leibniz parallelisable spaces, and hence maximally supersymmetric consistent truncations, is reduced to a simple algebraic problem. It is shown that the exceptional algebroid perspective also gives a simple description of Poisson–Lie U‐duality without spectators and hence of generalised Yang–Baxter deformations. [ABSTRACT FROM AUTHOR]

Modern cosmology has two competing theories of the origin of the universe: the "Singularity theory" and the "Superstring theory". Four Dilemmas of the "Superstring theory" are presented: the incompleteness of the eleven space–time dimensions, the inextricable dependence on the "Space–Time Background", the "Zero-Brane theory" admitting stuff smaller than the Planck scale, and the pure mathematical theory that cannot be falsified by experiments. Although the "Singularity theory" is faced with many critiques from the "Superstring theory", from the perspective of Information Ontology, treating the "Singularity" as "Origin Information" can dissolve these troubles well. For the "Singularity theory", the new philosophical thinking framework effectively explains the parameter problems of the universe, and gives satisfied response to the challenges from the "Superstring theory". As a result, the "Singularity theory" has a more competitive advantage on the origin of the universe. [ABSTRACT FROM AUTHOR]

The Fermi National Accelerator Laboratory (FNAL) recently announced confirmation of the Brookhaven National Lab (BNL) measurements of the g - 2 of the muon that uncovered a discrepancy with the theoretically calculated Standard Model value. We suggest an explanation for the combined BNL+FNAL 4.2 σ deviation within the supersymmetric grand unification theory (GUT) model No-Scale F - S U (5) supplemented with a string derived TeV-scale extra 10 + 10 ¯ vector-like multiplet and charged vector-like singlet (X E , X E c) , dubbed flippons. We introduced these vector-like particles into No-Scale Flipped SU(5) many years ago, and as a result, the renormalization group equation (RGE) running was immediately shaped to produce a distinctive and rather beneficial two-stage gauge coupling unification process to avoid the Landau pole and lift unification to the string scale, in addition to contributing through 1-loop to the light Higgs boson mass. The flippons have long stood ready to tackle another challenge, and now do so yet again, where the charged vector-like "lepton"/singlet couples with the muon, the supersymmetric down-type Higgs H d , and a singlet S, using a chirality flip to easily accommodate the muonic g - 2 discrepancy in No-Scale F - S U (5) . Considering the phenomenological success of this string derived model over the prior 11 years that remains accommodative of all presently available LHC limits plus all other experimental constraints, including no fine-tuning, and the fact that for the first time a Starobinsky-like inflationary model consistent with all cosmological data was derived from superstring theory in No-Scale Flipped SU(5), we believe it is imperative to reconcile the BNL+FNAL developments within the model space. [ABSTRACT FROM AUTHOR]

An alternative scenario about the phenomenology of primordial universe is k -inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely, the inflaton. In this paper, we focus on k -essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac–Born–Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein's gravity involving quantum corrections such as the Chern–Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein–Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble's parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis, it is proved that models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern–Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves are yet to be observed, if detected, compatibility with the aforementioned theory can be achieved. [ABSTRACT FROM AUTHOR]

String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry algebras in arbitrary dimension and signature, which generalizes the ideas underlying symplectic Majorana spinors. In our formalism R-symmetry acts on an auxiliary multiplicity space which makes its action manifest. This allows us to provide extensive tables which list the R-symmetry groups of extended supersymmetry algebras for all signatures together with other useful information. Twisted ('type-*') supersymmetry algebras in Lorentz signature with non-compact R-symmetry groups are shown to be part of a general pattern resulting from the interplay between complex superbrackets and reality conditions. As an application we show how the relations between type-II string theories in ten and nine dimensions can be extracted from their supersymmetry algebras. We also use our results to determine the special geometry of vector and hypermultiplet scalar manifolds of four-dimensional N = 2 and three-dimensional N = 4 supergravity theories for all signatures. [ABSTRACT FROM AUTHOR]

Following Gepner's approach, we propose a construction of models of tensor product orbifolds of the minimal models of two-dimensional field theory with superconformal symmetry. To build models that satisfy the requirements of modular invariance, we use a spectral flow transformation. We demonstrate this construction with a specific example and show that its application ensures the modular invariance of the partition function simultaneously with the mutual locality of the fields of the theory under consideration. [ABSTRACT FROM AUTHOR]