Supergravity Solutions Research Articles

Naked BPS singularities in AdS3 supergravity

Abstract anti-de Sitter (AdS) supergravity admits supersymmetric solutions that describe BPS defects. We investigate such solutions in AdS3 supergravity formulated as a Chern–Simons theory on OSp ( 2 | 1 ) × OSp ( 2 | 1 ) and compute the Killing spinor equation on the BTZ geometry, looking for BPS solutions on the entire space of parameters. We focus our attention on defects that represent geometries with integer angular excesses corresponding to specific negative values of the BTZ mass, extending other results in the literature to all real values of mass and angular momentum. We argue that, in the semiclassical limit, the BPS defects can be associated with degenerate representations of the Virasoro symmetry at the boundary. The case of non-diagonal representations, describing stationary, non-static defects, is also discussed.

The surprising structure of non-relativistic 11-dimensional supergravity

We study a non-relativistic limit of 11-dimensional supergravity. This limit leads to a theory with an underlying membrane Newton-Cartan geometry. Consistency of the non-relativistic limit requires the imposition of constraints, requiring that certain bosonic and fermionic torsions and curvatures vanish. We investigate the implications of two versions of these constraints. In one version, we keep only 16 supersymmetry transformations, leading to a simple (purely bosonic) constraint structure but an unusual realisation of the supersymmetry algebra which does not close into diffeomorphisms. In the other, we keep all 32 supersymmetry transformations. This requires a complicated sequence of bosonic and fermionic constraints, eventually involving three derivatives of bosonic fields. We argue, with a linearised calculation, that this sequence of constraints terminates. Furthermore, we show that there exists a family of supersymmetric solutions satisfying these constraints, containing the non-relativistic limit of the M2 supergravity solution recently obtained by Lambert and Smith as a background relevant for non-relativistic holography.

The General Supersymmetric Solution of Minimal Massive Supergravity

The General Supersymmetric Solution of Minimal Massive Supergravity

Supersymmetric black hole hair and AdS3× S3

The 4D-5D connection allows us to view the same near horizon geometry as part of a 4D black hole or a 5D black hole. A much studied example of this phenomenon is the BMPV black hole uplifted to 6D with flat base space versus Taub-NUT base space. These black holes have identical near horizon AdS3 × S3 geometry. In this paper, we study modes in AdS3 × S3 and identify those that correspond to supersymmetric hair modes in the full black hole spacetimes. We show that these modes satisfy non-normalisable boundary conditions in AdS3. The non-normalisable boundary conditions are different for different hair modes and for different asymptotic completion. We also discuss how the supersymmetric hair modes on BMPV black holes fit into the classification of supersymmetric solutions of 6D supergravity.

Superconformal monodromy defects in ABJM and mABJM theory

We study D = 11 supergravity solutions which are dual to one-dimensional superconformal defects in d = 3 SCFTs. We consider defects in ABJM theory with monodromy for U(1)4 ⊂ SO(8) global symmetry, as well as in \U0001d4a9 = 2 mABJM SCFT, which arises from the RG flow of a mass deformation of ABJM theory, with monodromy for U(1)3 ⊂ SU(3) × U(1) global symmetry. We show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow. In all cases we allow for the possibility of conical singularities at the location of the defect. Various physical observables of the defects are computed including the defects conformal weight and the partition function, as well as associated supersymmetric Renyi entropies.

The geometry of large charge multi-traces in N = 4 SYM

We construct a one-parameter family of half-BPS solutions of type IIB supergravity using a consistent truncation to gauged five-dimensional supergravity. For small values of the parameter, the solution reduces to the linear perturbation of AdS5 × S5 dual to the chiral primary operator in the stress-tensor multiplet, and we give evidence that the geometry is regular and asymptotes AdS in a normalisable way for arbitrarily large values of the parameter. We conjecture that the solution is the gravity dual of a “heavy” multi-trace operator in N = 4 SU(N) Super Yang-Mills made by p copies of the stress-tensor chiral primary operator, with p of order N2 in the large N limit. We perform some holographic checks supporting this duality map.

AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

AbstractThe author proceed to construct a dual pair for the background by applying non‐Abelian T‐duality (here as Poisson–Lie [PL] T‐duality on a semi‐Abelian double). By using a certain parametrization of the 4‐dimensional Lie group and by a suitable choice of spectator‐dependent matrices the original ‐model including the metric and a non‐trivial ‐field are constructed. The dual background constructed by means of the PL T‐duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non‐trivial ‐flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non‐Abelian T‐dual ‐models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two‐loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

Superconformal monodromy defects in 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}=4 SYM and LS theory

We study type IIB supergravity solutions that are dual to two-dimensional superconformal defects in d = 4 SCFTs which preserve 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} = (0, 2) supersymmetry. We consider solutions dual to defects in 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} = 4 SYM theory that have non-trivial monodromy for U(1)3 ⊂ SO(6) global symmetry and we also allow for the possibility of conical singularities. In addition, we consider the addition of fermionic and bosonic mass terms that have non trivial dependence on the spatial directions transverse to the defect, while preserving the superconformal symmetry of the defect. We compute various physical quantities including the central charges of the defect expressed as a function of the monodromy, the on-shell action as well as associated supersymmetric Rényi entropies. Analogous computations are carried out for superconformal defects in the 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, d = 4 Leigh-Strassler SCFT. We also show that the defects of the two SCFTs are connected by a line of bulk marginal mass deformations and argue that they are also related by bulk RG flow.

An S3 × S3 bundle over S4 and new supergravity solutions

The metric of S7 can be written as an SU(2)-instanton bundle over S4. It is also possible to write it differently as an anti-instanton bundle. We use this observation to construct an instanton–anti-instanton, SU(2)×SU(2), bundle over S4. We show that this 10d manifold admits two Einstein metrics. We then rewrite the metric to isolate two U(1) directions of the fibre and dimensionally reduce along them to get an eight dimensional metric describing an S2×S2 bundle over S4. This metric allows a harmonic 4-form which we use to derive new supergravity solutions in eleven and ten dimensions as AdS3×M8 and AdS2×M8, respectively.

Regularising spectral curves for homogeneous Yang-Baxter strings

In this Letter, we study the semi-classical spectrum of integrable worldsheet σ-models using the Spectral Curve. We consider a Homogeneous Yang-Baxter deformation of the AdS5×S5 superstring, understood as the composition of a Jordanian with a “non-diagonal” TsT deformation. We derive its type IIB supergravity solution, whose isometry algebra features zero supercharges and a non-relativistic conformal algebra in 0+1 dimensions. While the Spectral Curves of non-diagonal TsT models are ill-defined, we demonstrate that the composition with a Jordanian model regularises this issue. From the regularised Curve, we derive the one-loop shift of the classical energy and the semi-classical spectrum of excitations of a point-like string. In the TsT limit, the one-loop shift vanishes despite the loss of supersymmetry. Our results suggest that it may be possible to use standard Bethe Ansatze on spin chain pictures of deformed N=4 Super-Yang-Mills theory dual to non-diagonal TsT models.

SU(1,1) and SU(2) bundles on AdS4 and complex supergravity solutions

We study eleven dimensional supergravity solutions with an AdS7 factor. By writing AdS7 metric as an SU(1,1) bundle over AdS4 we derive new supergravity solutions. The solutions, however, are obtained in Euclidean signature and thus are necessarily complex. We also discuss AdS7 as an SU(2) bundle over AdS4, and observe that the two sets of solutions are related by analytic continuation of the scale factor of the fiber.

On the absence of supergravity solutions for localized, intersecting sources

For decades intersecting D-branes and O-planes have been playing a very important role in string phenomenology in the context of particle physics model building and in the context of flux compactifications. The corresponding supergravity equations are hard to solve so generically solutions only exist in a so-called smeared limit where the delta function sources are replaced by constants. We are showing here that supergravity solutions for two perpendicularly intersecting localized sources in flat space do not exist for a generic diagonal metric Ansatz. We show this for two intersecting sources with p = 1, 2, 3, 4, 5, 6 spatial dimensions that preserve 8 supercharges, and we allow for fully generic fluxes.

Spin-2 universal minimal solutions on type IIA and IIB supergravity

In this paper, we consider the spin-2 field perturbations of four families of supergravity solutions. These include AdS5 and AdS7 backgrounds of type IIA as well as AdS4 and AdS6 backgrounds of Type IIB. As the main result, we show that, in all the cases, there is a solution given by a combination of the warp factors. We also find the respective mass spectra. We analyze the normalizability of the solutions and identify the superconformal multiplets dual to them.

Supersymmetric AdS solitons and the interconnection of different vacua 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} = 4 Super Yang-Mills

We find AdS soliton solutions in 5-dimensional gauged supergravity, obtained from the S5 compactification of type IIB, with a dilaton saturating the Breitenlohner-Freedman bound. The solutions depend on the value of the periodicity of an S1 cycle and the boundary values for two U(1) gauge fields, and give a scalar VEV in the dual field theory. At certain values of the gauge sources we have supersymmetric solutions, corresponding to supersymmetric flows, which are a deformation of the Coulomb Branch flow in 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} = 4 SYM. The solutions parameterize quantum phase transitions between a discrete spectrum phase, a continuous above a mass gap phase, and a continuous without a mass gap phase, in 2+1 dimensions. We analyze the phase diagram in terms of the QFT sources and we find that for every value for them, there are always two branches of supergravity solutions. We find that these two branches of solitons correspond to two possible vacua existing in the dual QFT when fermions are anti-periodic on an S1. We describe the interconnection of these states in the QFT at strong ’t Hooft coupling in the large N limit. In 10 dimensions, our solutions are related to deformations of D3-brane distributions.

Euclidean flows, solitons, and wormholes in AdS space from M-theory

Multiparametric families of nonsupersymmetric EAdS4 flows as well as asymptotically EAdS4 solitons and wormholes are constructed within the four-dimensional SO(8) gauged supergravity that describes the compactification of M-theory on S7. More concretely, the solutions are found within the so-called STU model that describes the U(1)4 invariant sector of the theory. The on-shell action and gravitational free energy are computed for the regular solutions, the latter being zero for the wormholes irrespective of supersymmetry. There are special loci in parameter space yielding solutions with enhanced (super)symmetry. Examples include a supersymmetric EAdS4 flow with SO(4)×SO(4) symmetry dual to a specific real mass deformation of ABJM on S3 as well as a nonsupersymmetric wormhole with SU(3)×U(1)2 symmetry. Uplift formulas for these and other examples to Euclidean solutions of 11-dimensional supergravity are presented and their complex nature discussed. Published by the American Physical Society 2024

Holographic Weyl anomalies for 4d defects in 6d SCFTs

In this note, we study 1/4- and 1/2-BPS co-dimension two superconformal defects in the 6d 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} = (2, 0) AN−1 SCFT at large N using their holographic descriptions as solutions of 11d supergravity. In this regime, we are able to compute the defect contribution to the sphere entanglement entropy and the change in the stress-energy tensor one-point function due to the presence of the defect using holography. From these quantities, we are then able to unambiguously compute the values for two of the twenty-nine total Weyl anomaly coefficients that characterize 4d conformal defects in six and higher dimensions. We are able to demonstrate the consistency of the supergravity description of the defect theories with the average null energy condition on the field theory side. For each class of defects that we consider, we also show that the A-type Weyl anomaly coefficient is non-negative. Lastly, we uncover and resolve a discrepancy between the on-shell action of the 7d 1/4-BPS domain wall solutions and that of their 11d uplift.

U folds from geodesics in moduli space

We exploit the presence of moduli fields in the AdS3×S3×CY2, where CY2=T4 or K3, solution to type IIB superstring theory, to construct a U-fold solution with geometry AdS2×S1×S3×CY2. This is achieved by giving a nontrivial dependence of the moduli fields in SO(4,n)/SO(4)×SO(n) (n=4 for CY2=T4 and n=20 for CY2=K3), on the coordinate η of a compact direction S1 along the boundary of AdS3, so that these scalars, as functions of η, describe a geodesic on the corresponding moduli space. The backreaction of these evolving scalars on spacetime amounts to a splitting of AdS3 into AdS2×S1 with a nontrivial monodromy along S1 defined by the geodesic. Choosing the monodromy matrix in SO(4,n;Z), this supergravity solution is conjectured to be a consistent superstring background. We generalize this construction starting from an ungauged theory in D=2d, d odd, describing scalar fields nonminimally coupled to (d−1) forms and featuring solutions with topology AdSd×Sd, and moduli scalar fields. We show, in this general setting, that giving the moduli fields a geodesic dependence on the η coordinate of an S1 at the boundary of AdSd is sufficient to split this space into AdSd−1×S1, with a monodromy along S1 defined by the starting and ending points of the geodesic. This mechanism seems to be at work in the known J-fold solutions in D=10 type IIB theory and hints toward the existence of similar solutions in the type IIB theory compactified on CY2. We argue that the holographic dual theory on these backgrounds is a 1+0 CFT on an interface in the 1+1 theory at the boundary of the original AdS3. Published by the American Physical Society 2024

Supersymmetric Wormholes in String Theory.

We construct a large family of Euclidean supersymmetric wormhole solutions of type IIB supergravity which are asymptotically AdS_{5}×S^{5}. The solutions are constructed using consistent truncation to maximally gauged supergravity in five dimensions which is further truncated to a four scalar model. Within this model we perform a full analytic classification of supersymmetric domain wall solutions with flat Euclidean domain wall slices. On each side of the wormhole, the solution asymptotes to AdS_{5} dual to N=4 supersymmetric Yang-Mills deformed by a supersymmetric mass term.

Confinement and D5-branes

In this work we present new solutions of type IIB supergravity based on wrapped D5 branes. We propose that two of these backgrounds are holographically dual to Quantum Field Theories that confine. The high energy regime of the field theories is that of a Little String Theory. We study various observables (Wilson and ’t Hooft loops, Entanglement entropy, density of degrees of freedom and the spectrum of spin-two glueballs, among others). We also present two new black membrane backgrounds and analyse some thermodynamic aspects of these solutions.

The Heterotic-Ricci Flow and Its Three-Dimensional Solitons

We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}, for a complete Riemannian metric and a three-form H on a manifold M. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion H. When κ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa = 0$$\\end{document} the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when H=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H=0$$\\end{document} and κ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa >0$$\\end{document} the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form H. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining, in particular, the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton and leave as open the construction of a Heterotic soliton with non-constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.