11D Supergravity Research Articles

Taming the 11D pure spinor b-ghost

We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these operators, it will be straightforwardly shown that left{Q,bright}=frac{P^2}{2} , as well as {b, b} = QΩ. As an application of this novel formulation, the ghost number two vertex operator will easily be obtained in a completely covariant manner from a standard descent relation, the ghost number three vertex operator will be shown to satisfy the generalized Siegel gauge condition, and the 11D supergravity two-particle superfield will be constructed in a quite simple way.

The discrete Green-Schwarz mechanism in 6D F-theory and elliptic genera of non-critical strings

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a ’t Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

Generalized 11D supergravity equations from tri-vector deformations

In Bakhmatov et al. (Phys. Rev. D 105(8): L081904, 2022) we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full technical details of that result which is based on SL(5) exceptional field theory. The equations are obtained by making a non-unimodular tri-vector Yang-Baxter deformation which breaks the initial local diffeomorphism symmetry in 11 dimensions down to separate coordinate transformations in external 7 and internal 4 directions. We also give some non-trivial solutions to these equations.

Universal accelerating cosmologies from 10d supergravity

We study 4d Friedmann-Lemaître-Robertson-Walker cosmologies obtained from time-dependent compactifications of Type IIA 10d supergravity on various classes of 6d manifolds (Calabi-Yau, Einstein, Einstein-Kähler). The cosmologies we present are universal in that they do not depend on the detailed features of the compactification manifold, but only on the properties which are common to all the manifolds belonging to that class. Once the equations of motion are rewritten as an appropriate dynamical system, the existence of solutions featuring a phase of accelerated expansion is made manifest. The fixed points of this dynamical system, as well as the trajectories on the boundary of the phase space, correspond to analytic solutions which we determine explicitly. Furthermore, some of the resulting cosmologies exhibit eternal or semi-eternal acceleration, whereas others allow for a parametric control on the number of e-foldings. At future infinity, one can achieve both large volume and weak string coupling. Moreover, we find several smooth accelerating cosmologies without Big Bang singularities: the universe is contracting in the cosmological past (T < 0), expanding in the future (T > 0), while in the vicinity of T = 0 it becomes de Sitter in hyperbolic slicing. We also obtain several cosmologies featuring an infinite number of cycles of alternating periods of accelerated and decelerated expansions.

Properties of the moduli set of complete connected projective special real manifolds

We construct a compact convex generating set \(\mathcal {C}_n\) of the moduli set of closed connected projective special real manifolds of fixed dimension n. We show that a closed connected projective special real manifold corresponds to an inner point of \(\mathcal {C}_n\) if and only if it has regular boundary behaviour. Our results can be used to describe deformations of 5d supergravity theories with complete scalar geometries.

Linearized off-shell 4+7 supergeometry of 11D supergravity

We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, G2-structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This is complemented by a top-down description of the linearized supergeometry of the 4|4 + 7 superspace dealing directly with torsion, curvature, and Bianchi identities. Torsion constraints that (combined with the Bianchi identities) lead to the preceding prepotential expressions of the gauge fields are identified. All irreducible consequences of the torsion and 4-form Bianchi identities are systematically derived except for dimension 2 Bianchi identities of the 4-form, and dimension frac{5}{2} Bianchi identities of torsion, which set bosonic curls of components of one lower dimension to zero.

Lyapunov exponents in [formula omitted] supersymmetric Jackiw-Teitelboim gravity

We study N=2 supersymmetric Jackiw-Teitelboim (JT) gravity at finite temperature coupled to matter. The matter fields are related to superconformal primaries by AdS/CFT duality. Due to broken super reparametrisation invariance in the SCFT dual, there are corrections to superconformal correlators. These are generated by the exchange of super-Schwarzian modes which is dual to the exchange of 2D supergravity modes. We compute corrections to four-point functions for superconformal primaries and analyse the behaviour of out-of-time-ordered correlators. In particular, four-point functions of two pairs of primaries with mutually vanishing two-point functions are considered. By decomposing the corresponding supermultiplet into its components, we find different Lyapunov exponents. The value of the Lyapunov exponents depends on whether the correction is due to graviton, gravitini or graviphoton exchange. If mutual two-point functions do not vanish all components grow with maximal Lyapunov exponent.

ABJM at finite N via 4d supergravity

We apply the conjecture of [1] for gravitational building blocks to the effective supergravity description of M-theory on S7/ℤk. Utilizing known localization results for the holographically dual ABJM theory, we determine a complete tower of higher derivative corrections to the AdS4 supergravity and a further set of quantum corrections. This uniquely fixes the gravitational block, leading to holographic predictions for a number of exact ABJM observables, excluding only constant and non-perturbative corrections in the gauge group rank N. The predicted S3 partition function is an Airy function that reproduces previous results and generalizes them to include arbitrary squashing and mass deformations/R-charge assignments. The topologically twisted and superconformal indices are instead products of two different Airy functions, in agreement with direct numeric calculations in the unrefined limit of the former object. The general fixed-point formula for an arbitrary supersymmetric background is similarly given as a product of Airy functions.

Type IIB supergravity action on M5×X5 solutions

While the 10d type IIB supergravity action evaluated on AdS$_5\times S^5$ solution vanishes, the 5d effective action reconstructed from the equations of motion using $M^5 \times S^5$ compactification ansatz is proportional to the AdS$_5$ volume. The latter is consistent with the conformal anomaly interpretation in AdS/CFT context. We show that this paradox can be resolved if, in the case of $M^5 \times X^5$ topology, the 10d action contains an additional 5-form dependent "topological" term $\int F_{5M} \wedge F_{5X}$. The presence of this term is suggested also by gauge-invariance considerations in the PST formulation of type IIB supergravity action. We show that this term contributes to the 10d action evaluated on the D3-brane solution.

Harmonic forms on asymptotically ADS metrics

In this paper we study the rotationally invariant harmonic cohomology of a two-parameter family of Einstein metrics g which admits a cohomogeneity one action of SU(2) × U(1) and has AdS asymptotics. Depending on the values of the parameters, g is either of NUT type, if the fixed-point locus of the U(1) action is zero-dimensional, or of bolt type, if it is two-dimensional. We find that if g is of NUT type then the space of SU(2)-invariant harmonic two-forms is three-dimensional and consists entirely of self-dual forms; if g is of bolt type it is four-dimensional. In both cases we explicitly determine a basis. The pair (g, F) for F a self-dual harmonic two-form is also a solution of the bosonic sector of 4D supergravity. We determine for which choices it is a supersymmetric solution and the amount of preserved supersymmetry.

Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation

We classified in [1] certain 10d supergravity solutions with a 4d de Sitter, Minkowski or anti-de Sitter spacetime. We then found new solutions in previously unexplored classes. In this paper we study their properties, compare them to swampland conjectures, and make new observations.Using new numerical tools, we first identify all Lie algebras underlying the 6d group manifolds, allowing us to discuss their compactness. We then investigate scale separation, and prove related no-go theorems. Last but not least, we automatize and analyze the stability of all solutions. This leads us to propose the Massless Minkowski Conjecture, claiming the systematic presence of a 4d flat direction.

Non-topological logarithmic corrections in minimal gauged supergravity

We compute the logarithmic correction to the entropy of asymptotically AdS4 black holes in minimal mathcal{N} = 2 gauged supergravity. We show that for extremal black holes the logarithmic correction computed in the near horizon geometry agrees with the result in the full geometry up to zero mode contributions, thus clarifying where the quantum degrees of freedom lie in AdS spacetimes. In contrast to flat space, we observe that the logarithmic correction for supersymmetric black holes can be non-topological in AdS as it is controlled by additional four-derivative terms other than the Euler density. The available microscopic data and results in 11d supergravity indicate that the full logarithmic correction is topological, which suggests that the topological nature of logarithmic corrections could serve as a diagnosis of whether a low-energy gravity theory admits an ultraviolet completion.

Positive Energy and Non-SUSY Flows in ISO(7) Gauged Supergravity

We consider maximal gauged supergravity in 4D with the ISO(7) gauge group, which arises from a consistent truncation of massive IIA supergravity on a six-sphere. Within its G2-invariant sector, the theory is known to possess a supersymmetric AdS extremum, as well as two non-supersymmetric ones. In this context, we provide a first-order formulation of the theory by making use of the Hamilton–Jacobi (HJ) formalism. This allows us to derive a positive energy theorem for both non-supersymmetric extrema. Subsequently, we also find novel non-supersymmetric domain walls (DWs) interpolating between the supersymmetric extremum and each of the other two. Finally, we discuss a perturbative HJ technique that may be used in order to solve for curved DW geometries.

M2-branes on discs and multi-charged spindles

We study supersymmetric AdS2 × Y9 solutions of 11d supergravity where Y9 is an S7 fibration over a Riemann surface equipped with a metric of non-constant curvature. We consider two classes of Riemann surface: the first is a spindle and the second is a topological disc. These solutions are interpreted as the near-horizon limit of M2 branes wrapped on the Riemann surface and describe the near-horizon of a 4d black hole. In the case of the topological disc there are additional flavour M2 branes smeared on a five-sphere embedded in the transverse S7. We perform a full global analysis of both classes of solutions, both from a 4d and an 11d viewpoint. Finally we compute the two-dimensional Newton’s constant from which we obtain a prediction for the entropy of the black hole.

AdS5 holography and higher-derivative supergravity

We study four-derivative corrections to 5d mathcal{N} = 2 minimal gauged supergravity using tools from conformal supergravity. There are two supersymmetric invariants at the four-derivative order and we show explicitly how to write down the action in the Poincaré frame in terms of their coefficients. We apply our results in the context of holography where the four-derivative terms in the supergravity action translate into corrections to the conformal anomalies of the dual 4d mathcal{N} = 1 SCFT. We use these results to study corrections to the entropy of the supersymmetric black string solutions of minimal supergravity. We also discuss explicit embeddings of the 5d supergravity in string and M-theory and use them to fix the higher-derivative coefficients in terms of the microscopic parameters.

Hbox {AdS}_3 holography for non-BPS geometries

By using the approach introduced in Ganchev et al. (Q-Balls Meet Fuzzballs: Non-BPS Microstate Geometries. arXiv:2107.09677 [hep-th]) we construct non-BPS solutions of 6D (1, 0) supergravity coupled to two tensor multiplets as a perturbation of hbox {AdS}_3times S^3. These solutions are both regular and asymptotically hbox {AdS}_3times S^3, so according to the standard holographic framework they must have a dual CFT interpretation as non-supersymmetric heavy operators of the D1–D5 CFT. We provide quantitative evidence that such heavy CFT operators are bound states of a large number of light BPS operators that are mutually non-BPS.

Flavor symmetries and automatic enhancement in the 6D supergravity swampland

We argue for the quantum-gravitational inconsistency of certain 6d $\mathcal{N}=(1,0)$ supergravity theories, whose anomaly-free gauge algebra $\mathfrak{g}$ and hypermultiplet spectrum $M$ were observed in arxiv:2012.01437 to be realizable only as part of a larger gauge sector $(\mathfrak{g}' \supset \mathfrak{g}, M' \supset M)$ in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such $(\mathfrak{g},M)$ theories are not compatible with quantum gravity constraints, and how the "automatic enhancement" to $(\mathfrak{g}', M')$ remedies this. In the first class of models, with $\mathfrak{g}' = \mathfrak{g} \oplus \mathfrak{h}$, we show that there exists an unbroken flavor symmetry $\mathfrak{h}$ acting on the matter $M$, which, if ungauged, would violate the No-Global-Symmetries Hypothesis. This argument also applies to 1-form center symmetries, which govern the gauge group topology and massive states in representations different than those of massless states. In a second class, we find that $\mathfrak{g}$ is incompatible with the flavor symmetry of certain BPS strings that must exist by the Completeness Hypothesis.

Spin structures and AdS4 holography

We study the importance of spin structures as defining data for 11d supergravity backgrounds of the form AdS4 × S7/Zk with a free orbifold action. For a generic choice of the orbifold action, there is only one spin structure that preserves invariant Killing spinors. There are, however, orbifold actions that allow for more than one spin structure with preserved Killing spinors. In these cases the two different spin structures should lead to distinct holographically dual 3d SCFTs with different amounts of supersymmetry. We illustrate this phenomenon by studying the KK spectrum of 11d supergravity on AdS4 × S7/Z4. For one choice of spin structure this background is dual to the 3d mathcal{N} = 6 ABJM theory at level k = 4. For the alternative choice of spin structure our results suggest that the holographic dual is a different 3d mathcal{N} = 2 SCFT and we discuss some of its properties.

Scale-separated AdS4 vacua of IIA orientifolds and M-theory

We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.

Near-AdS2 Spectroscopy: Classifying the Spectrum of Operators and Interactions in N=2 4D Supergravity

We describe holographic properties of near-AdS2 spacetimes that arise within spherically symmetric configurations of N=2 4D U(1)4 supergravity for both gauged and ungauged theories. These theories pose a rich space of AdS2×S2 backgrounds, and their responses in the near-AdS2 region are not universal. In particular, we show that the spectrum of operators is dual to the matter fields, and their cubic interactions are sensitive to properties of the background and the theory it is embedded in. The properties that have the most striking effect are whether the background is supersymmetric or not and if the theory is gauged or ungauged. Interesting effects are due to the appearance of operators with Δ&lt;2, which depending on the background, can lead to, for instance, instabilities or extremal correlators. The resulting differences will have an imprint on the quantum nature of the microstates of near-extremal black holes, reflecting that not all extremal black holes respond equally when kicked away from extremality.