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In the Emergence Proposal in QG it is conjectured that all light-particle kinetic terms are absent in the fundamental UV theory and are generated by quantum corrections in the IR. It has been argued that this may provide for some microscopic understanding of the WGC and SDC. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any EFT coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in $d$ spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d $\mathcal{N}=2$ theories arising from type IIA on a CY$_3$, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY$_3$ or a $K3$ surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in QG as an intrinsic IR phenomenon., v2: minor changes and typos corrected. 79 pages + Appendices, 11 figures, 8 tables

We study the non-linear structure of Type IIB eight-derivative couplings involving the metric and the complexified three-form $G_3$. We show that, at the level of five-point string amplitudes, the kinematics in the maximally R-symmetry-violating sector is fully matched by standard superspace integrals and by superparticle amplitudes in M-theory on a two-torus. The latter approach is used to determine the complete effective action in this sector and to verify its invariance under SL$(2,\mathbb{Z})$ duality. We further comment on the general structure of the higher-point kinematics. Compactifications to lower dimensions provide both tests for our results and the arena for their applications. We verify that K3 reductions are fully consistent with the constraints of six-dimensional supersymmetry, and derive the four-dimensional flux scalar potential and axion kinetic terms at order $(\alpha^{\prime})^{3}$ in Calabi-Yau threefold reductions., Comment: 34 pages plus appendices

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability works for supersymmetric vacua, where it is widely expected to hold. We first show that the nucleation of brane bubbles in type II AdS compactifications is forbidden in the probe approximation by a simple argument involving pure spinors and calibrations. We then adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, also showing how to consistently include localised sources. We finally initiate an analysis of how these arguments might be extended to non-supersymmetric vacua. In M-theory, at the lower-derivative level, we find that the most natural modifications fail to stabilize the skew-whiffed and Englert vacua., Comment: v2: References added, published version, 32+16 pages

In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an $SU(1,3)$ spacetime symmetry in the presence of instantons. We explicitly show how $SU(1,3)$ is enhanced to $SU(1,3)\times U(1)$ where the additional $U(1)$ acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters., 40 pages. Technical details added in Section 3, and notation adjusted. Matches JHEP published version

We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in $AdS_4$ and are important for the corresponding ${\mathcal N} =1$ supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in $AdS_4$ was derived for this compactification. Some comments are also made concerning the $G_2$ holonomy and its implications on the structure of the operator equations on the squashed seven-sphere., Comment: 28 pages, v2: typos corrected, a footnote added

By fibering the duality between the E8 × E8 heterotic string on T3 and M-theory on K3, we study heterotic duals of M-theory compactified on G2 orbifolds of the form T7/$$ {\mathbb{Z}}_2^3 $$ ℤ 2 3 . While the heterotic compactification space is straightforward, the description of the gauge bundle is subtle, involving the physics of point-like instantons on orbifold singularities. By comparing the gauge groups of the dual theories, we deduce behavior of a “half-G2” limit, which is the M-theory analog of the stable degeneration limit of F-theory. The heterotic backgrounds exhibit point-like instantons that are localized on pairs of orbifold loci, similar to the “gauge-locking” phenomenon seen in Hořava-Witten compactifications. In this way, the geometry of the G2 orbifold is translated to bundle data in the heterotic background. While the instanton configuration looks surprising from the perspective of the E8 × E8 heterotic string, it may be understood as T-dual Spin(32)/ℤ2 instantons along with winding shifts originating in a dual Type I compactification.

A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d$$ \mathcal{N} $$ N = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an $SU(1,3)$ conformal symmetry. These actions have a Lagrange multiplier which imposes a novel $\Omega$-deformed anti-self-dual gauge field constraint. Using a generalised 't Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface., Comment: 39 pages, 7 figures

The involutory subalgebra K(E$_9$) of the affine Kac-Moody algebra E$_9$ was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions arXiv:2102.00870. We revisit these representations and describe their associated ideals in more detail, with particular emphasis on two chiral versions that can be constructed for each such representation. For every such unfaithful representation we show that the action of K(E$_9$) decomposes into a direct sum of two mutually commuting (`chiral' and `anti-chiral') parabolic algebras with Levi subalgebra $\mathfrak{so}(16)_+\,\oplus\,\mathfrak{so}(16)_-$. We also spell out the consistency conditions for uplifting such representations to unfaithful representations of K(E$_{10}$). From these results it is evident that the holonomy groups so far discussed in the literature are mere shadows (in a Platonic sense) of a much larger structure., 22 pages. v2: minor modifications and updated references; JHEP version

Obtaining the values of the coupling constants of the low energy effective theory corresponding to QCD, compatible with experimental data, even in the (vector) mesonic sector from (the $$ \mathcal{M} $$ M -theory uplift of) a UV-complete string theory dual, has thus far been missing in the literature. We take the first step in this direction by obtaining the values of the coupling constants of the $$ \mathcal{O} $$ O (p4) χPT Lagrangian in the chiral limit involving the NGBs and ρ meson (and its flavor partners) from the $$ \mathcal{M} $$ M -theory/type IIA dual of large-N thermal QCD, inclusive of the $$ \mathcal{O} $$ O (R4) corrections. We observe that ensuring compatibility with phenomenological/lattice results (the values) as given in [1], requires a relationship relating the $$ \mathcal{O} $$ O (R4) corrections and large-N suppression. In other words, QCD demands that the higher derivative corrections and the large-N suppressed corrections in its M/string theory dual, are related. As a bonus, we explicitly show that the $$ \mathcal{O} $$ O (R4) corrections in the UV to the $$ \mathcal{M} $$ M -theory uplift of the type IIB dual of large-N thermal QCD at low temperatures, can be consistently set to be vanishingly small.

We study the large $ N$ sign oscillation of the twisted indices for 3D theories of class $\mathcal{R}$ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt$_{\pm}$ with $p=0$, which are Wick rotation of magnetically charged AdS$_4$ black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the $F\wedge F$-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold., 13 pages

In arXiv:1911.08172 we have studied the single-particle free energy of a class of Little String Theories of A-type, which are engineered by $N$ parallel M5-branes on a circle. To leading instanton order (from the perspective of the low energy $U(N)$ gauge theory) and partially also to higher order, a decomposition was observed, which resembles a Feynman diagrammatic expansion: external states are given by expansion coefficients of the $N=1$ BPS free energy and a quasi-Jacobi form that governs the BPS-counting of an M5-brane coupling to two M2-branes. The effective coupling functions were written as infinite series and similarities to modular graph functions were remarked. In the current work we continue and extend this study: Working with the full non-perturbative BPS free energy, we analyse in detail the cases $N=2,3$ and $4$. We argue that in these cases to leading instanton order all coupling functions can be written as a simple combination of two-point functions of a single free scalar field on the torus. We provide closed form expressions, which we conjecture to hold for generic $N$. To higher instanton order, we observe that a decomposition of the free energy in terms of higher point functions with the same external states is still possible but a priori not unique. We nevertheless provide evidence that tentative coupling functions are still combinations of scalar Greens functions, which are decorated with derivatives or multiplied with holomorphic Eisenstein series. We interpret these decorations as corrections of the leading order effective couplings and in particular link the latter to dihedral graph functions with bivalent vertices, which suggests an interpretation in terms of disconnected graphs., 50 pages

We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest $SL(2)$ symmetry)., Comment: 34 pages; v2: minor changes, references added; v3: JHEP published version

We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 5D, N=1 M-theory and the 4D type II superstring. This theory is a complexification of the fundamental 5-brane theory that embeds the 4D, N=1 M-theory of the 3D type II string in a sense that we make explicit at the level of the Lagrangian and Hamiltonian formulations. We find three types of section condition: in spacetime, on the worldvolume, and one tying them together. The 5-brane theory is recovered from the new theory by a double dimensional reduction.

Glauber-Sudarshan states, sometimes simply referred to as Glauber states, or alternatively as coherent and squeezed-coherent states, are interesting states in the configuration spaces of any quantum field theories, that closely resemble classical trajectories in space-time. In this paper, we identify four-dimensional de Sitter space as a coherent state over a supersymmetric Minkowski vacuum. Although such an identification is not new, what is new however is the claim that this is realizable in full string theory, but only in conjunction with temporally varying degrees of freedom and quantum corrections resulting from them. Furthermore, fluctuations over the de Sitter space is governed by a generalized graviton (and flux)-added coherent state, also known as the Agarwal-Tara state. The realization of de Sitter space as a state, and not as a vacuum, resolves many issues associated with its entropy, zero-point energy and trans-Planckian censorship, amongst other things., Comment: 124 pages, 1 figure; v2: Typos corrected and references added; v3: Some approximate results in sec 3.2 replaced by exact ones, typos corrected and references updated; v4: sec 3.3 elaborated, typos corrected and references updated. Final version to appear in JHEP

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type $(G, G')$., Comment: 64 pages; v2: fixed typos, added references and clarifications. v3: more references added; v4: fixed refs and typos, JHEP version; v5: small corrections and updated references

An axion-like particle (ALP) with mass mϕ ∼ 10−15 eV oscillates with frequency ∼1 Hz. This mass scale lies in an open window of astrophysical constraints, and appears naturally as a consequence of grand unification (GUT) in string/M-theory. However, with a GUT-scale decay constant such an ALP overcloses the Universe, and cannot solve the strong CP problem. In this paper, we present a two axion model in which the 1 Hz ALP constitutes the entirety of the dark matter (DM) while the QCD axion solves the strong CP problem but contributes negligibly to the DM relic density. The mechanism to achieve the correct relic densities relies on low-scale inflation (mϕ ≲ Hinf ≲ 1 MeV), and we present explicit realisations of such a model. The scale in the axion potential leading to the 1 Hz axion generates a value for the strong CP phase which oscillates around $$ {\overline{\theta}}_{\mathrm{QCD}}\sim {10}^{-12} $$ θ ¯ QCD ∼ 10 − 12 , within reach of the proton storage ring electric dipole moment experiment. The 1 Hz axion is also in reach of near future laboratory and astrophysical searches.

We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data., v3 (JHEP submission): minor typos corrected, improved discussion in Appendix A and D

We perform a general reduction of an M5-brane on a spacetime that admits a null Killing vector, including couplings to background 4-form fluxes and possible twisting of the normal bundle. We give the non-abelian extension of this action and present its supersymmetry transformations. The result is a class of supersymmetric non-Lorentzian gauge theories in 4+1 dimensions, which depend on the geometry of the six-dimensional spacetime. These can be used for DLCQ constructions of M5-branes reduced on various manifolds.

We determine 5d $\mathcal{N}=1$ SCFTs originating from 6d $(E_n,E_m)$ conformal matter theories with $n\neq m$ by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers., 36 pages, 12 figures

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d $\mathcal{N}=1$ SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d $\mathcal{N}=1$ SYM theory, where we recover it from a mixed 't Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed 't Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities., 48 pages. v2: Added references and fixed typos

We study the possibility of realizing scale-separated type IIB Anti-de Sitter and de Sitter compactifications within a controlled effective field theory regime defined by low-energy and large (but scale-separated) compactification volume. The approach we use views effective theories as truncations of the full quantum equations of motion expanded in a trans-series around this asymptotic regime. By studying the scalings of all possible perturbative and non-perturbative corrections we identify the effects that have the right scaling to allow for the desired solutions. In the case of Anti-de Sitter, we find agreement with KKLT-type scenarios, and argue that non-perturbative brane-instantons wrapping four-cycles (or similarly scaling effects) are essentially the only ingredient that allows for scale separated solutions. We also comment on the relation of these results to the AdS swampland conjectures. For the de Sitter case we find that we are forced to introduce an infinite number of relatively unsuppressed corrections to the equations of motion, leading to a breakdown of effective theory. This suggests that if de Sitter vacua exist in the string landscape, they should not be thought of as residing within the same effective theory as the AdS or Minkowski compactifications, but rather as defining a separate asymptotic regime, presumably related to the others by a duality transformation., Comment: 24 pages, v2 changes to the scaling analysis in section 3.4, references added

We investigate finite-$N$ corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the contribution of extended M5-branes in the dual geometry $AdS_4\times \boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on $N$ M5-branes we calculate the indices by analyzing extended M2-branes in $AdS_7\times \boldsymbol{S}^4$. Again, we include only configurations with single wrapping. We first compare the result for $N=1$ with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of $A_{N-1}$ theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index., Comment: 40 pages; v2: minor corrections

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in $G_2$ holonomy spaces and to $Spin(7)$ metrics on 8-manifolds with $T^2$ fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories $T[M_4]$ on the other., Comment: 38 pages, 19 figures

It is known that matrix models computing the partition functions of three-dimensional $\mathcal{N}=4$ superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results., Comment: 51 pages, 1 figure

In this note, we study the Swampland Distance Conjecture in TCS $G_2$ manifold compactifications of M-theory. In particular, we are interested in testing a refined version -- the Emergent String Conjecture, in settings with 4d $N=1$ supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the $K3$-fibre in a TCS $G_2$ manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fibre via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS $G_2$ compactifications, which might lead to a weakly coupled fundamental type II string theory., Comment: 24 pages. V2: Reference added, Typos corrected, several details on the dualities filled. Published version

We present a nonabelian Lagrangian that appears to have $(2,0)$ superconformal symmetry and that can be coupled to a supergravity background. But for our construction to work, we have to break this superconformal symmetry by imposing as a constraint on top of the Lagrangian that the fields have vanishing Lie derivatives along a Killing direction., Comment: 30 pages

In this work we analyze F-theory and Type IIB orientifold compactifications to study α′-corrections to the four-dimensional, N $$ \mathcal{N} $$ = 1 effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the G 2 R 3 and (∇G)2 R 2-sector in eleven-dimensions relevant in Calabi-Yau fourfold reductions. We suggest that the three-dimensional, N $$ \mathcal{N} $$ = 2 Kähler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi-Yau fourfold. The divisor integral Ansatz for the Kähler potential and Kähler coordinates may be lifted to four-dimensional, N $$ \mathcal{N} $$ = 1 F-theory vacua. We identify a novel correction to the Kähler potential and coordinates at order α′ 2, which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of D7-branes and O7-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel α′-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.

The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver descriptions of the geometry. Embedding into M-theory, a large class of dualities of 3d $\mathcal{N}=2$ theories associated to quivers is obtained. The multi-cover skein relation admits a compact formulation in terms of quantum torus algebras associated to the quiver and in this language the relations are similar to wall-crossing identities of Kontsevich and Soibelman., 43+5 pages

We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum Field Theories in even dimensions that can be geometrically engineered from M5-branes. Our approach is based on anomaly inflow, and characterizes the anomaly polynomial of the QFT in terms of the geometric definition of the field theory. In particular, when the QFT admits a holographic dual, the topological data of the solution is sufficient to compute the anomalies of the dual field theory, including finite terms in $N$. We study several classes of examples in four and six dimensions, with or without known M5-brane probe configurations., Comment: 31 pages plus appendices

By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d $(2,0)$ theory on a three-manifold $M_3$. This generalization is applicable to both the 3d $\mathcal{N}=2$ and $\mathcal{N}=1$ supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by $M_3$. This is carried out in detail for $M_3$ a Seifert manifold, where we compute a refined version of the Witten index. In the context of the 3d-3d correspondence, we complement this analysis in the dual topological theory, and determine the refined counting of flat connections on $M_3$, which matches the Witten index computation that takes the higher-form symmetries into account., Comment: 101 pages, 11 figures

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the C-field in Cohomotopy theory implies a list of expected anomaly cancellation conditions, including: shifted C-field flux quantization and C-field tadpole cancellation, but also the DMW anomaly cancellation and the C-field's integral equation of motion., 55 pages; v2: proof of fluxed tadpole cancellation added; v3: exposition reorganized, discussion of M5 brane backgrounds postponed to a subsequent article arXiv:2002.07737, title and abstract adjusted accordingly; v4: published version

It was recently discovered that for a boundary system in the presence of a background magnetic field, the quantum fluctuation of the vacuum would create a non-uniform magnetization density for the vacuum and a magnetization current is induced in the vacuum. It was also shown that this "magnetic Casimir effect" of the vacuum is closely related to another quantum effect of the vacuum, the Weyl anomaly. Furthermore, the phenomena can be understood in terms of the holography of the boundary system. In this paper, we generalize this four dimensional effect to six dimensions. We use the AdS/BCFT holography to show that in the presence of a 3-form magnetic field strength $H$,a string current is induced in a six dimensional boundary conformal field theory. This allows us to determine the gauge field contribution to the Weyl anomaly in six dimensional conformal field theory in a $H$-flux background. For the (2,0) superconformal field theory of $N$ M5-branes, the current has a magnitude proportional to $N^3$ for large $N$. This suggests that the degree of freedoms scales as $N^3$ in the (2,0) superconformal theory of $N$ multiple M5-branes. The prediction we have for the Weyl anomaly is a new criteria that the (2,0) theory should satisfy., Comment: 19 pages, 2 figures, match the published version in JHEP

We complete the classification of Mink$_4$ solutions preserving $\mathcal{N}=2$ supersymmetry and SU(2) R-symmetry parameterised by a round $S^2$ factor. We consider eleven-dimensional supergravity and relax the assumptions of earlier works in type II theories. We show that, using chains of dualities, all solutions of this type can be generated from one of two master classes: an SU(2)-structure in M-theory and a conformal Calabi-Yau in type IIB. Finally, using our results, we recover AdS$_5\times S^2$ solutions in M-theory and construct a compact Minkowski solution with Atiyah-Hitchin singularity., 30 pages + appendices, 2 figures. v3: published version

We obtain cosmological solutions with Kasner-like asymptotics in $$ \mathcal{N} $$ N = 2 gauged and ungauged supergravity by maximal analytic continuation of planar versions of non-extremal black hole solutions. Initially, we construct static solutions with planar symmetry by solving the time-reduced field equations. Upon lifting back to four dimensions, the resulting static regions are incomplete and bounded by a curvature singularity on one side and a Killing horizon on the other. Analytic continuation reveals the existence of dynamic patches in the past and future, with Kasner-like asymptotics. For the ungauged STU-model, our solutions contain previously known solutions with the same conformal diagram as a subset. We find explicit lifts to five, six, ten and eleven dimensions which show that in the extremal limit, the underlying brane configuration is the same as for STU black holes. The extremal limit of the six-dimensional lift is shown to be BPS for special choices of the integration constants. We argue that there is a universal correspondence between spherically symmetric black hole solutions and planar cosmological solutions which can be illustrated using the Reissner-Nordström solution of Einstein-Maxwell theory.

The Swampland Distance Conjecture suggests that an infinite tower of modes becomes exponentially light when approaching a point that is at infinite proper distance in field space. In this paper we investigate this conjecture in the K\"ahler moduli spaces of Calabi-Yau threefold compactifications and further elucidate the proposal that the infinite tower of states is generated by the discrete symmetries associated to infinite distance points. In the large volume regime the infinite tower of states is generated by the action of the local monodromy matrices and encoded by an orbit of D-brane charges. We express these monodromy matrices in terms of the triple intersection numbers to classify the infinite distance points and construct the associated infinite charge orbits that become massless. We then turn to a detailed study of charge orbits in elliptically fibered Calabi-Yau threefolds. We argue that for these geometries the modular symmetry in the moduli space can be used to transfer the large volume orbits to the small elliptic fiber regime. The resulting orbits can be used in compactifications of M-theory that are dual to F-theory compactifications including an additional circle. In particular, we show that there are always charge orbits satisfying the distance conjecture that correspond to Kaluza-Klein towers along that circle. Integrating out the KK towers yields an infinite distance in the moduli space thereby supporting the idea of emergence in that context., Comment: 47 pages, 1 figure, 4 tables. v2:minor modifications and references added

M-theory on $AdS_7 \times S^4$ admits a description where the $AdS_7$ factor is constructed as a timelike Hopf fibration over a non-compact three dimensional complex projective space $\tilde{\mathbb{CP}}^3$. We consider the worldvolume theory for M5-branes at a fixed $\tilde{\mathbb{CP}}^3$ radius which, after reduction along the timelike fibre, is given by an $\Omega$-deformed Yang-Mills theory with eight supercharges. Taking the radius to infinity then induces a classical RG flow. We construct the fixed point action which has an enhanced 24 supercharges and which can be understood as the $(2,0)$ theory of M5-branes on flat space reduced along a compact null Killing direction., Comment: 21 pages, typos corrected, references added

According to a conjecture, all 5d SCFTs should be obtainable by rank-preserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a "parent" Calabi-Yau threefold which captures the Coulomb branch of the compactified 6d SCFT. The RG flows to 5d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to "descendant" Calabi-Yau threefolds which describe the Coulomb branches of the resulting 5d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d SCFTs. Since 6d SCFTs of arbitrary rank can be viewed as being constructed out of rank one SCFTs, we accomplish the extension to arbitrary rank by identifying a prescription for gluing together Calabi-Yaus associated to rank one 6d SCFTs., Comment: 83 pages, v2: references and typos corrected, the mathematica file "Pushforward.nb" now attached as an ancillary file v3: Geometries for SO(11,12), F_4 corrected. Gluing rules for Sp---SO(odd) corrected. Missing SU(3)+SU(3) E-string gluing added v4: References and clarifications

In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest., Comment: 146 pages, lots of figures, v2: typos corrected, v3: JHEP published version, v4: typo in def 3.1 fixed

A suitable generalisation of the Lichnerowicz formula can relate the squares of supersymmetric operators to the effective action, the Bianchi identities for fluxes, and some equations of motion. Recently, such formulae have also been shown to underlie the (generalised) geometry of supersymmetric theories. In this paper, we derive an M-theoretic Lichnerowicz formula that describes eleven-dimensional supergravity together with its higher-derivative couplings. The first corrections to the action appear at eight-derivative level, and the construction yields two different supersymmetric invariants, each with a free coefficient. We discuss the restriction of our construction to seven-dimensional internal spaces, and implications for compactifications on manifolds of $G_2$ holonomy. Inclusion of fluxes and computation of contributions with higher than eight derivatives are also discussed., 35 pages

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs., Comment: 119 pages, 10 figures and 20 tables

In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called `exotic branes'---low codimension objects with highly non-perturbative tensions, scaling as $g_s^{\alpha}$ for $\alpha \leq -3$. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT)---collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string- and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist., Comment: 73 pages Latex, v2: citations added, some orbits corrected