Supergravity Background Research Articles

Inclusion of statistical matter in the nonrelativistic limit of NS-NS supergravity

We combine techniques from kinetic theory and string dualities to couple statistical matter to a nonrelativistic supergravity background, enabling the theory to be formulated in a T-duality invariant form. Similarly to the relativistic case, we explicitly demonstrate that, in the nonrelativistic limit, the many-strings system necessitates a viscous fluid description for describing the statistical matter. This is achieved coupling a generalized energy-momentum tensor in the framework of double field theory, which it is covariant under T-duality transformations. Published by the American Physical Society 2024

Four-point correlators in N = 4 SYM from AdS5 bubbling geometries

Four-point correlation functions are observables of significant interest in holographic field theories. We compute an infinite family of four-point correlation functions of operators in short multiplets of 4D N = 4 super Yang-Mills theory in the supergravity regime, by studying the quadratic fluctuations around non-trivial supergravity backgrounds. The supergravity backgrounds are supersymmetric smooth geometries in the family derived by Lin, Lunin and Maldacena. The light probes comprise an infinite sequence of Kaluza-Klein harmonics of the dilaton/axion. For generic parameter values, the supergravity backgrounds are dual to heavy CFT states. However we focus on the limit in which the dual CFT states become light single-particle states. The resulting all-light four-point correlators are related by superconformal Ward identities to previously known four-point correlators of half-BPS chiral primary operators. By verifying that the Ward identities are satisfied, we confirm the validity of the supergravity method.

Flux quantization on M5-branes

We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac’s charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5’s flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 “super-embeddings”. Finally, assuming the flux-quantization law to actually be in co-Homotopy (“Hypothesis H”) we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of “open M5-branes” in heterotic M-theory.

JT gravity from non-Abelian T-duality

We study the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp(1|2). While the initial model represents an appropriate 3D supergravity background, interpretable as the superspace version of AdS3, the T-dual model fails solving the 3D supergravity torsion constraints. We argue that this has to do with a factorisation pattern taking place under dualisation: the dual 3D geometry can be rewritten as the supersymmetric version of AdS2, satisfying the supergravity constraints, fibered over what we interpret as the superspace equivalent of the standard bosonic line. We discuss an interesting connection between T-duals of generic Principal Chiral Models and Poisson sigma models. We exploit it to show that in a suitable limit the dual action studied in this work gives rise to JT (super)gravity.

Integrability and non-integrability for holographic dual of matrix model and non-Abelian T-dual of AdS5×S5

In this paper we study integrability and non-integrability for type-IIA supergravity background dual to deformed plane wave matrix model. From the bulk perspective, we estimate various chaos indicators that clearly shows chaotic string dynamics in the limit of small value of the parameter L present in the theory. On the other hand, the string dynamics exhibits a non-chaotic motion for the large value of the parameter L and therefore presumably an underlying integrable structure. Our findings reveal that the parameter L in the type-IIA background acts as an interpolation between a non-integrable theory to an integrable theory in dual SCFTs.

Hierarchy of curvatures in exceptional geometry

Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We show that to construct it, a hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy. This approach allows to define generalized homogeneous spaces which underlie generalized U-duality, admit consistent truncations and provide a huge class of new flux backgrounds with nontrivial structure groups. Published by the American Physical Society 2024

A compendium of logarithmic corrections in AdS/CFT

We study the logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS4. Our results also have important implications for effective field theory coupled to gravity in AdS4 and for the existence of scale-separated AdS4 vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.

Supersymmetric Casimir energy on N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 conformal supergravity backgrounds

We provide a first principles derivation of the supersymmetric Casimir energy of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 SCFTs in four dimensions using the supercharge algebra on general conformal supergravity backgrounds that admit Killing spinors. The superconformal Ward identities imply that there exists a continuous family of conserved R-currents on supersymmetric backgrounds, as well as a continuous family of conserved currents for each conformal Killing vector. These continuous families interpolate between the consistent and covariant R-current and energy-momentum tensor. The resulting Casimir energy, therefore, depends on two continuous parameters corresponding to the choice of conserved currents used to define the energy and R-charge. This ambiguity is in addition to any possible scheme dependence due to local terms in the effective action. As an application, we evaluate the general expression for the supersymmetric Casimir energy we obtain on a family of backgrounds with the cylinder topology ℝ × S3 and admitting a single Majorana supercharge. Our result is a direct consequence of the supersymmetry algebra, yet it resembles more known expressions for the non-supersymmetric Casimir energy on such backgrounds and differs from the supersymmetric Casimir energy obtained from the zero temperature limit of supersymmetric partition functions. We defer a thorough analysis of the relation between these results to future work.

Worldsheet description of a massive type IIA superstring in 10D

We construct, following [1, 2], a massive M2-brane (supermembrane) as the limit of a genus two M2-brane that becomes a twice punctured Riemann surface with particular boundary conditions on the fields defined on the punctures. The target space is M9 × LCD, where LCD is a genus one light cone diagram. It contains mass terms and a topological term associated with the non-triviality of the target surface that, at low energies, can be associated with the presence of a cosmological constant. We show that the supergravity background of the M2-brane considered in this formulation requires the presence of M9-branes acting as sources. They correspond to the 11D uplift of the characteristic D8’s of Romans supergravity. To this end, we explicitly show that some of the background singularities of the massive M2-brane can be reproduced by the M9-branes found by [3]. This establishes a relation between the Romans mass and the moduli of the massive M2-brane.When dimensionally reduced, we obtain a worldsheet Hamiltonian of a N=2 type IIA closed superstring in 10D. We denote it massive string. The corresponding massive string inherits a non-vanishing constant term from the topological massive M2-brane that shifts the Hamiltonian. The non-vanishing parameter is related to the non-trivial structure of the massive M2-brane background and it can be related to the Romans mass term. It also contains a modified tension due to the non-trivial dependence on the moduli and on the punctures associated with the target torus.

Nonrelativistic expansion of type IIA NS5 brane

We carry out nonrelativistic expansion for NS5 brane based on a codimension two foliation of type IIA supergravity background. We simultaneously expand the world-volume fields in an appropriate 1/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 1/c^2 $$\\end{document} expansion together with the background fluxes. When put together, the resulting procedure yields a finite world-volume action for nonrelativistic NS5 brane that is coupled to String Newton-Cartan background.

A 4d non-BPS NS-NS microstate

We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of a certain number of decoupled (i.e. gs → 0) NS5 branes wrapping T3 × S1 × S1 with fundamental strings wrapping non-contractable cycles of S1 × S1 with integer momentum modes along them. We show that perturbative worldsheet theory in this background is given by a null-gauged WZW model. We also show that the consistency of the worldsheet theory imposes non-trivial constraints on the supergravity background.

Matrix models and holography: Mass deformations of long quiver theories in 5d and 3d

We enlarge the dictionary between matrix models for long linear quivers preserving eight supercharges in d=5d=5 and d=3d=3 and type IIB supergravity backgrounds with AdS_{d+1}d+1 factors. We introduce mass deformations of the field theory that break the quiver into a collection of interacting linear quivers, which are decoupled at the end of the RG flow. We find and solve a Laplace problem in supergravity which realises these deformations holographically. The free energy and expectation values of antisymmetric Wilson loops are calculated on both sides of the proposed duality, finding agreement. With our matching procedure, the free energy satisfies a strong version of the F-theorem.

Semiclassical quantization of the superstring and Hagedorn temperature

In a recent paper [1], the semiclassical quantization of a string, winding once around the compact Euclidean time circle, on a supergravity background dual to the deep infrared regime of a confining finite temperature gauge theory, was carried out. The string mass-shell condition and, by extrapolation, the Hagedorn temperature to leading order in the holographic limit was deduced. In this work, we improve on those results in three ways. First, we fix some missing details of the related light-cone quantization analysis. Second, we reconsider the problem under the lens of a background-covariant geometrical formalism. This allows us to put the semiclassical mass-shell condition on more solid grounds. Finally, going beyond the semiclassical regime, we compute the Hagedorn temperature at next-to-leading order in the holographic limit. The sub-leading correction turns out to arise entirely from the contribution of the zero modes of the massive worldsheet scalar fields. Our result matches that of a recent analysis in the literature based on the Horowitz-Polchinski stringy star effective model.

Localization on AdS3× S2. Part I. The 4d/5d connection in off-shell Euclidean supergravity

We begin to develop the formalism of localization for the functional integral of supergravity on AdS3× S2. We show how the condition of supersymmetry in the Euclidean ℍ3/ℤ × S2 geometry naturally leads to a twist of the S2 around the time direction of AdS3. The twist gives us a five-dimensional Euclidean supergravity background dual to the elliptic genus of (0, 4) SCFT2 at the semiclassical level. On this background we set up the off-shell BPS equations for one of the Killing spinors, such that the functional integral of five-dimensional Euclidean supergravity on ℍ3/ℤ × S2 localizes to its space of solutions. We obtain a class of solutions to these equations by lifting known off-shell BPS solutions of 4-dimensional supergravity on AdS2× S2. In order to do this consistently, we construct and use a Euclidean version of the off-shell 4d/5d lift of arXiv:1112.5371, which could be of independent interest.

Decomposable (5, 6)-solutions in eleven-dimensional supergravity

We present decomposable (5, 6)-solutions M̃1,4×M6 in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogy of the work performed by Chrysikos and Galaev [Classical Quantum Gravity 37, 125004 (2020)], who made similar computations for decomposable (6, 5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with a negative Einstein constant (in the “mostly plus” convention) and Riemannian Kähler–Einstein manifolds with a positive Einstein constant. This conclusion generalizes a result of Pope and van Nieuwenhuizen [Commun. Math. Phys. 122, 281–292 (1989)] concerning the appearance of six-dimensional Kähler–Einstein manifolds in eleven-dimensional supergravity. In this setting, we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein–Sasakian structures with a negative Einstein constant on the 5-sphere, known from the work of Boyer et al. [Commun. Math. Phys. 262, 177–208 (2006)].

N = (2, 0) AdS3 solutions of M-theory

We consider the most general solutions of eleven-dimensional supergravity preserving N = 2 supersymmetry whose metrics are warped products of three-dimensional anti-de Sitter space with an eight-dimensional manifold, focusing on those realising (2,0) superconformal symmetry. We give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local SU(2) structure and its intrinsic torsion. We show that these supergravity backgrounds always admit a nowhere-vanishing Killing vector field that preserves the solution and encodes the U(1) R-symmetry of the dual field theory. We illustrate our results with examples which have appeared in the literature, including those with SU(4), G2 and SU(3) structures, and discuss new classes of Minkowski solutions.

Double field theory with matter and the generalized Bergshoeff–de Roo identification

The scalar field-perfect fluid (sf-pf) correspondence shows that the energy-momentum tensor of a scalar field is in correspondence with the dynamics of a perfect fluid. In this work we generalize this concept to study the higher-derivative structure of double field theory with statistical matter. Using the generalized Bergshoeff--de Roo identification we find nontrivial higher-derivative corrections for the generalized scalar field Lagrangian. However, these contributions are removed to any desired order using field redefinitions at the supergravity level. By virtue of the generalized sf-pf correspondence we obtain the higher-derivative dynamics for the perfect fluid in the double geometry, which is also trivialized at the supergravity level. These results imply that the well-known ${\ensuremath{\alpha}}^{\ensuremath{'}}$-corrections obtained by this procedure only correct the effective vacuum Lagrangian, while the sf-pf Lagrangian coupled to the supergravity background remains uncorrected to all orders. Our findings apply for a general (bosonic-heterotic-type II-HSZ) supergravity background.

Holographic duals of the mathcal{N} = 1* gauge theory

We use the long-wavelength effective theory of black branes (blackfold approach) to perturbatively construct holographic duals of the vacua of the mathcal{N} = 1* supersymmetric gauge theory. Employing the mechanism of Polchinski and Strassler, we consider wrapped black five-brane probes with D3-brane charge moving in the perturbative supergravity back-grounds corresponding to the high- and low-temperature phases of the gauge theory. Our approach recovers the results for the brane potentials and equilibrium configurations known in the literature in the extremal limit, while away from extremality we find metastable black D3-NS5 configurations with horizon topology ℝ3 × \U0001d54a2 × \U0001d54a3 in certain regimes of parameter space, which cloak potential brane singularities. We uncover novel features of the phase diagram of the mathcal{N} = 1* gauge theory in different ensembles and provide further evidence for the appearance of metastable states in holographic backgrounds dual to confining gauge theories.

Bi-η and bi-λ deformations of ℤ4 permutation supercosets

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

SUSY and Tri-Vector Deformations

We analyze conditions for a tri-vector deformation of a supergravity background to preserve some supersymmetry. Working in the formalism of the SL(5) exceptional field theory, we present its supersymmetry transformations and introduce an additional USp(4) transformation to stay in the supergravity frame. This transformation acts on local indices and deforms BPS equations of exceptional field theory. The requirement for the deformation to vanish is the desired condition. The condition is shown to be consistent with previous results on bi-vector deformations.