AdS Solutions Research Articles

Properties of the new mathcal{N} = 1 AdS4 vacuum of maximal supergravity

The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional mathcal{N} = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new mathcal{N} = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × ℤ2-invariant truncation of the mathcal{N} = 8 theory to an mathcal{N} = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the mathcal{N} = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × ℤ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional {mathbb{Z}}_2^3 -invariant scalar manifold (SU(1, 1)/U(1))7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new mathcal{N} = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an mathcal{N} = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

AdS3 solutions in massive IIA with small mathcal{N} = (4, 0) supersymmetry

We study AdS3 x S 2 solutions in massive IIA that preserve small mathcal{N} = (4, 0) supersymmetry in terms of an SU(2)-structure on the remaining internal space. We find two new classes of solutions that are warped products of the form AdS3 x S2 x M4 x ℝ. For the first, M4=CY2 and we find a generalisation of a D4-D8 system involving possible additional branes. For the second, M4 need only be Kahler, and we find a generalisation of the T-dual of solutions based on D3-branes wrapping curves in the base of an elliptically fibered Calabi-Yau 3-fold. Within these classes we find many new locally compact solutions that are foliations of AdS3 x S2 x CY2 over an interval, bounded by various D brane and O plane behaviours. We comment on how these local solutions may be used as the building blocks of infinite classes of global solutions glued together with defect branes. Utilising T-duality we find two new classes of AdS3 x S3 x M4 solutions in liB. The first backreacts D5s and KK monopoles on the D1-D5 near horizon. The second is a generalisation of the solutions based on D3-branes wrapping curves in the base of an elliptically fibered CY3 that includes non trivial 3-form flux.

Two dimensional mathcal{N} = (0, 4) quivers dual to AdS3 solutions in massive IIA

In this paper we discuss an infinite family of new solutions in massive Type IIA supergravity with AdS3×S2 factors, preserving mathcal{N} = (0, 4) SUSY. After studying geometrical aspects of the backgrounds we propose a duality with a precise family of quivers that flow to (0,4) fixed points at low energies. These quivers consist on two families of (4,4) linear quivers coupled by matter fields. We present various tests of our proposal.

Anomaly inflow, accidental symmetry, and spontaneous symmetry breaking

We consider the 6d (1,0) SCFT on a stack of N M5-branes probing a ℂ2/ℤ2 singularity. In particular, we study its compactifications to four dimensions on a smooth genus-g Riemann surface with non-trivial flavor flux, yielding a family of 4d CFTs. By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a U(1) generator. These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. These phenomena leave an imprint on the ’t Hooft anomaly polynomial of the 4d CFTs, which is obtained from recently developed anomaly inflow methods in M-theory [1]. In the large-N limit, we identify the gravity dual of the 4d setups to be a class of smooth AdS5 solutions first discussed by Gauntlett-Martelli-Sparks-Waldram. Using our anomaly polynomial, we compute the conformal central charge and a non-Abelian flavor central charge at large N , finding agreement with the holographic predictions.

AdS3 solutions in massive IIA, defect CFTs and T-duality

We establish a map between AdS3×S2 and AdS7 solutions to massive IIA supergravity that allows one to interpret the former as holographic duals to D2-D4 defects inside 6d (1,0) CFTs. This relation singles out in a particular manner the AdS3×S2 solution constructed from AdS3×S3×CY2 through non-Abelian T-duality, with respect to a freely acting SU(2). We find explicit global completions to this solution and provide well-defined (0,4) 2d dual CFTs associated to them. These completions consist of linear quivers with colour groups coming from D2 and D6 branes and flavour groups coming from D8 and D4 branes. Finally, we discuss the relation with flows interpolating between AdS3×S2×T4 geometries and AdS7 solutions found in the literature.

S-folds and (non-)supersymmetric Janus solutions

The S-fold description of Janus-type solutions of type IIB supergravity is investigated. This is done by first studying a U(1) × U (1) invariant sector of the four­ dimensional dyonically-gauged [SO(1) × SO(6)] × ℝ12 maximal supergravity that arises upon reduction of type IIB supergravity on ℝ × S5. Two AdS4 solutions preserving SU(3) and SO (6) gauge symmetry together with mathcal{N} = 1 and mathcal{N} = 0 supersymmetry are found within this sector. Fetching techniques from the E 7(7) exceptional field theory, these solutions are uplifted to ten-dimensional S-folds of type IIB Janus-type solutions of the form AdS4 × ℝ × M5. The solutions presented here are natural candidates for the holographic duals of three-dimensional mathcal{N} = 1 and mathcal{N} = 0 interface super-Yang-Mills theories with SU(3) and SU(4) internal symmetry.

Consistent KK truncations for M5-branes wrapped on Riemann surfaces

We construct a consistent Kaluza–Klein reduction of D = 11 supergravity on , where or H2, or a quotient thereof, at the level of the bosonic fields. The result is a gauged N = 4, D = 5 supergravity theory coupled to three vector multiplets, with the gauging lying in an subgroup of the global symmetry group of the ungauged theory. For , the D = 5 theory has a maximally supersymmetric AdS5 vacuum which uplifts to the known solution of D = 11 supergravity corresponding to M5-branes wrapping a Riemann surface with genus greater than one and dual to an N = 2 SCFT in d = 4. For , we find two AdS5 solutions, one of which is new, and both of which are unstable. There is an additional subtruncation to an N = 2 gauged supergravity coupled to two vector multiplets, with very special real manifold , and a single hypermultiplet, with quaternionic Kähler manifold and gauging associated with an subgroup.

Minimal D = 4 mathcal{N} = 2 supergravity from D = 11: an M-theory free lunch

ABSTRACTWe present a new consistent truncation of D = 11 supergravity to D = 4 mathcal{N} = 2 minimal gauged supergravity, on the seven-dimensional internal Riemannian space corresponding to the most general class of D = 11 solutions with an AdS4 factor and mathcal{N} = 2 supersymmetry. A truncation ansatz is proposed and its consistency checked at the level of the D = 11 Bianchi identity, bosonic equations of motion, and supersymmetry variations of the gravitino. The general class includes an mathcal{N} = 2 AdS4 solution dual to the conformal, low-energy physics phase corresponding to a mass deformation of the M2-brane field theory. A consistent truncation recently constructed on this particular geometry is recovered from our formalism.

Deforming black holes with even multipolar differential rotation boundary

Motivated by the novel asymptotically global AdS4 solutions with deforming horizon in [21], we analyze the boundary metric with even multipolar differential rotation and numerically construct a family of deforming solutions with quadrupolar differential rotation boundary, including two classes of solutions: solitons and black holes. In contrast o solutions with dipolar differential rotation boundary, we find that even though the norm of Killing vector ∂t becomes spacelike for certain regions of polar angle θ when ε > 2, solitons and black holes with quadrupolar differential rotation still exist and do not develop hair due to superradiance. Moreover, at the same temperature, the horizonal deformation of quadrupolar rotation is smaller than that of dipolar rotation. Furthermore, we also study the entropy and quasinormal modes of the solutions, which have the analogous properties to that of dipolar rotation.

Spin 2 operators in holographic 4d mathcal{N}=2 SCFTs

A broad class of holographic duals for 4d mathcal{N}=2 SCFTs is based on the general half-BPS AdS5 solutions to M-theory constructed by Lin, Lunin and Maldacena, and their Kaluza-Klein reductions to Type IIA. We derive the equations governing spin 2 fluctuations around these solutions. The resulting partial differential equations admit families of universal solutions which are constructed entirely out of the generic data characterizing the background. This implies the existence of families of spin 2 operators in the dual SCFTs, in short superconformal multiplets which we identify.

Quantum null energy condition and its (non)saturation in 2d CFTs

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions of AdS_33 Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT_22 with a global quench dual to AdS_33-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS_33 dual to a primary operator of dimension h in a large central charge expansion and explicitly compute both, the backreacted Ryu–Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by h/4h/4 in the large h expansion.

The moduli spaces of S-fold CFTs

An S-fold has played an important role in constructing supersymmetric field theories with interesting features. It can be viewed as a type of AdS4 solutions of Type IIB string theory where the fields in overlapping patches are glued by elements of SL(2, ℤ). This paper examines three dimensional quiver theories that arise from brane configurations with an inclusion of the S-fold. An important feature of such a quiver is that it contains a link, which is the T (U(N)) theory, between two U(N) groups, along with bifundamental and fundamental hypermultiplets. We systematically study the moduli spaces of those quiver theories, including the cases in which the non-zero Chern-Simons levels are turned on. A number of such moduli spaces turns out to have a very rich structure and tells us about the brane dynamics in the presence of an S-fold.

Holographic duals of five-dimensional SCFTs on a Riemann surface

We study the twisted compactifications of five-dimensional Seiberg SCFTs, with {mathrm{SU}}_{mathrm{mathcal{M}}}(2)times {E}_{N_f}+1 flavor symmetry, on a generic Riemann surface that preserves four supercharges. The five-dimensional SCFTs are obtained from the decoupling limit of N D4-branes probing a geometry of Nf < 8 D8-branes and an O8-plane. In addition to the R-symmetry, we can also twist the flavor symmetry by turning on background flux on the Riemann surface. In particular, in the string theory construction of the five-dimensional SCFTs, the background flux for the SUℳ(2) has a geometric origin, similar to the topological twist of the R-symmetry. We argue that the resulting low-energy three-dimensional theories describe the dynamics on the world-volume of the N D4-branes wrapped on the Riemann surface in the O8/D8 background. The Riemann surface can be described as a curve in a Calabi-Yau three-fold that is a sum of two line bundles over it. This allows for an explicit construction of AdS4 solutions in massive IIA supergravity dual to the world-volume theories, thereby providing strong evidence that the three-dimensional SCFTs exist in the low-energy limit of the compactification of the five-dimensional SCFTs. We compute observables such as the free energy and the scaling dimensions of operators dual to D2-brane probes; these have non-trivial dependence on the twist parameter for the U(1) in SUℳ(2). The free energy exhibits the N5/2 scaling that is emblematic of five-dimensional SCFTs.

Marginal deformations of 3d mathcal{N}=2 CFTs from AdS4 backgrounds in generalised geometry

We study exactly marginal deformations of 3d mathcal{N}=2 CFTs dual to AdS4 solutions in eleven-dimensional supergravity using generalised geometry. Focussing on Sasaki-Einstein backgrounds, we find that marginal deformations correspond to turning on a four-form flux on the internal space at first order. Viewing this as the deformation of a generalised structure, we derive a general expression for the four-form flux in terms of a holomorphic function. We discuss the explicit examples of S7, Q1,1,1 and M1,1,1 and, using an obstruction analysis, find the conditions for the first-order deformations to extend all orders, thus identifying which marginal deformations are exactly marginal. We also show how the all-orders γ-deformation of Lunin and Maldacena can be encoded as a tri-vector deformation in generalised geometry and outline how to recover the supergravity solution from the generalised metric.

A massive class of mathcal{N}=2 AdS4 IIA solutions

We initiate a classification of mathcal{N}=2 supersymmetric AdS4 solutions of (massive) type IIA supergravity. The internal space is locally equipped with either an SU(2) or an identity structure. We focus on the SU(2) structure and determine the conditions it satisfies, dictated by supersymmetry. Imposing as an Ansatz that the internal space is complex, we reduce the problem of finding solutions to a Riccati ODE, which we solve analytically. We obtain in this fashion a large number of new families of solutions, both regular as well as with localized O8-planes and conical Calabi-Yau singularities. We also recover many solutions already discussed in the literature.

The geometry of mathcal{N}=3 AdS4 in massive IIA

The geometry of the mathcal{N}=3 , SO(4)-invariant, AdS4 solution of massive type IIA supergravity that uplifts from the mathcal{N}=3 vacuum of D = 4 mathcal{N}=8 dyonic ISO(7) supergravity is investigated. Firstly, a D = 4, SO(4)-invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)-invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the mathcal{N}=3 AdS4 solution in massive IIA and analyse its geometry. Locally, the internal S6 geometry corresponds to a warped fibration of S2 and a hemisphere of S4. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the mathcal{N}=3 solution are constructed and shown to obey the massive type IIA Killing spinor equations.

Magnetically-charged supersymmetric flows of gauged mathcal{N}=8 supergravity in five dimensions

We study magnetically-charged supersymmetric flow equations in a consistent truncation of gauged mathcal{N}=8 supergravity in five dimensions. This truncation gives gauged mathcal{N}=2 supergravity coupled to two vector multiplets and two hypermultiplets. We derive magnetically-charged flow equations of scalar fields from vector and hypermultiplets. It turns out that there could be only up to two nontrivial scalar fields out of eight from the hypermultiplets. Along the way, we recover some known AdS3 solutions of the flow equations.

A non-existence theorem for N > 16 supersymmetric AdS3 backgrounds

We show that there are no smooth warped AdS3 solutions in 10- and 11- dimensional supergravities which preserve strictly more than 16 supersymmetries and have internal space a compact without boundary manifold.

Holographic duals of 3d S-fold CFTs

We construct non-geometric AdS4 solutions of IIB string theory where the fields in overlapping patches are glued by elements of the S-duality group. We obtain them by suitable quotients of compact and non-compact geometric solutions. The quotient procedure suggests CFT duals as quiver theories with links involving the so-called T [U(N)] theory. We test the validity of the non-geometric solutions (and of our proposed holographic duality) by computing the three-sphere partition function Z of the CFTs. A first class of solutions is obtained by an S-duality quotient of Janus-type non-compact solutions and is dual to 3d mathcal{N}=4 SCFTs; for these we manage to compute Z of the dual CFT at finite N, and it agrees perfectly with the supergravity result in the large N limit. A second class has five-branes, it is obtained by a Möbius-like S-quotient of ordinary compact solutions and is dual to 3d mathcal{N}=3 SCFTs. For these, Z agrees with the supergravity result if one chooses the limit carefully so that the effect of the fivebranes does not backreact on the entire geometry. Other limits suggest the existence of IIA duals.

F-theory and AdS3/CFT2 (2, 0)

We continue to develop the program initiated in [1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d mathcal{N}=left(0,2right) supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold {mathcal{Y}}_8^{tau } , which is elliptically fibered over a base {tilde{mathrm{mathcal{M}}}}_6 . We construct two classes of solutions given in terms of a product ansatz tilde{{mathrm{mathcal{M}}}_6}=varSigma times {mathrm{M}}_4 , where Σ is a complex curve and {tilde{mathrm{mathcal{M}}}}_4 is locally a Kähler surface. In the first class {tilde{mathrm{mathcal{M}}}}_4 is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3 × K3 × ℳ5τ, dual to 2d (0, 2) SCFTs, and AdS3 × S3/Γ × CY3, dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d mathcal{N}=left(2,2right) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d mathcal{N}=1 SCFTs.