The most detailed constructions of microstate geometries, and particularly of superstrata, are done using $\mathcal{N} = (1,0)$ supergravity coupled to two anti-self-dual tensor multiplets in six dimensions. We show that an important sub-sector of this theory has a consistent truncation to a particular gauged supergravity in three dimensions. Our consistent truncation is closely related to those recently laid out by Samtleben and Sarioglu (arXiv:1907.08413 [hep-th]), which enables us to develop complete uplift formulae from the three-dimensional theory to six dimensions. We also find a new family of multi-mode superstrata, indexed by two arbitrary holomorphic functions of one complex variable, that live within our consistent truncation and use this family to provide extensive tests of our consistent truncation. We discuss some of the future applications of having an intrinsically three-dimensional formulation of a significant class of microstate geometries.
We quantize the D1-D5-P microstate geometries known as superstrata directly in supergravity. We use Rychkov's consistency condition [hep-th/0512053] which was derived for the D1-D5 system; for superstrata, this condition turns out to be strong enough to fix the symplectic form uniquely. For the $(1,0,n)$ superstrata, we further confirm this quantization by a bona-fide explicit computation of the symplectic form using the semi-classical covariant quantization method in supergravity. We use the resulting quantizations to count the known supergravity superstrata states, finding agreement with pre…
We compute one point functions of chiral primary operators in the D1-D5 orbifold CFT, in classes of states corresponding to microstates of two and three charge black holes. Black hole microstates describable by supergravity solutions correspond to coherent superpositions of states in the orbifold theory and we develop methods for approximating one point functions in such superpositions in the large N limit. We show that microstates built from long strings (large twist operators) have one point functions that are suppressed by powers of N. Accordingly, even when these microstates admit supergra…
We quantize the moduli space of regular D1-D5 microstates, directly from Type IIB SUGRA. The moduli space is parametrized by a smooth closed non-selfintersecting curve in four dimensions, and we derive that the components of the curve satisfy chiral boson commutation relations, with the correct value of the effective Planck constant previously conjectured using U-duality. We use the Crnkovic-Witten-Zuckerman covariant quantization method, previously used to quantize the `bubbling AdS' geometries, combined with a certain new `consistency condition' which allows us to reduce the computation to q…
We demonstrate a solution generating technique, modulo some constraints, for a large class of smooth supergravity solutions with the same asymptotic charges as a five dimensional 3-charge BPS black hole or black ring, dual to a D1/D5/P system. These solutions are characterized by a harmonic function with both positive and negative poles, which induces a geometric transition whereby singular sources have disappeared and all of the net charge at infinity is sourced by fluxes through two-cycles joining the poles of the harmonic function.
We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravit…
Magnetic and Dyonic solutions are constructed for the theory of abelian gauged N=2 gauged four dimensional supergravity coupled to vector multiplets. The solutions found preserve 1/4 of the supersymmetry.
We consider conformal defect solutions in four dimensional $N=2$ gauged supergravity. These solutions are constructed as a warped product of $AdS_2\times S^1$ over an interval with non-trivial electric and magnetic fields. We show for minimal gauged supergravity and for gauged supergravity with vector multiplets and abelian gauging that supersymmetric defect solutions are only possible when the geometry has a conical defect in either the bulk or the boundary metric.
We obtain the complete non-linear Kaluza-Klein ansatz for the reduction of the bosonic sector of massive type IIA supergravity to the Romans F(4) gauged supergravity in six dimensions. The latter arises as a consistent warped S^4 reduction.
The U(1) gauged version of the Strominger-Vafa five dimensional N=2 supergravity with one vector multiplet is obtained via dimensional reduction from the N=1 ten dimensional supergavity. Using such explicit relation between the gauged supergravity theory and ten dimensional supergravity, all known solutions of the five dimensional theory can be lifted up to ten-dimensions. The eleven dimensional solutions can also obtained by lifting the ten-dimensional solutions.
We obtain the explicit and complete bosonic non-linear Kaluza-Klein ansatz for the consistent S^4 reduction of D=11 supergravity to N=1, D=7 gauged supergravity. This provides a geometrical interpretation of the lower dimensional solutions from the eleven-dimensional point of view.
Magnetic BPS string solutions preserving quarter of supersymmetry are obtained for all abelian gauged d=5 N=2 supergravity theories coupled to vector supermultiplets. Due to a ``generalised Dirac quantization'' condition satisfied by the minimized magnetic central charge, the string metric takes a universal form for all five dimensional gauged theories.
The topologically twisted index for ABJM theory with gauge group $U(N)_k \times U(N)_{-k}$ has recently been shown, in the large-$N$ limit, to reproduce the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS$_4$ black holes. We numerically study the index beyond the large-$N$ limit and provide evidence that it contains a subleading logarithmic term of the form $-1/2\log N$. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answ…
Solutions describing holographic surface defects in $D=5,N=4$ gauged supergravity theories are constructed. It is shown that a surface defect solution in pure Romans' gauged supergravity is singular. Adding a single vector multiplet allows for the construction of a non-singular solution. The on-shell action and one point functions of operators in the presence of the defect are computed using holographic renormalization.
We consider the interplay of duality symmetries and gauged isometries of supergravity models giving N-extended, spontaneously broken supergravity with a no-scale structure. Some examples, motivated by superstring and M-theory compactifications are described.
BPS domain wall solutions of gauged supergravities are found, including those theories which have non-compact gauge groups. These include models that have both an unstable de Sitter solution and stable domain wall solutions.
We present some multiplets of N=2 off-shell supergravity in five dimensions. One is the Super Yang-Mills multiplet, another one is the linear multiplet. The latter one is used to establish a general action formula from which we derive an action for the Super Yang-Mills multiplet. The Super Yang-Mills multiplet is used to construct the nonlinear multiplet with gauged SU(2). This nonlinear multiplet and the action formula for the Yang-Mills multiplet enable us to write down an SU(2) gauged supergravity which we finally truncate to arrive at gauged supergravity with gauge group SO(2).
It is shown that N=4 gauged supergravity in four dimensions is obtained by compactifying N=1 supergravity in ten dimensions on the group manifold $S^3\times S^3$. This could be further related to supergravity in eleven dimensions. Analysis of supersymmetry conditions of N=4 gauged supergravity in four dimensions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field. These solutions are lifted to solutions of the ten and eleven dimensional theories.
We report on the gauged supergravity interpretation of certain compactifications of superstring theories with p-form fluxes turned on. We discuss in particular the interplay of duality symmetries in type IIB orientifolds and gauged isometries in the corresponding supergravity models. Turning on fluxes is generally described by the gauging of some nilpotent Lie group whose generators correspond to axion symmetries of R-R and N-S scalars.
We obtain a unified picture for the conifold singularity resolution. We propose that gauged supergravity, through a novel prescription for the twisting, provides an appropriate framework to smooth out singularities in the context of gravity duals of supersymmetric gauge theories.
We show that a generalised reduction of D=10 IIB supergravity leads, in a certain limit, to a maximally extended SO(2) gauged supergravity in D=9. We show the scalar potential of this model allows both Minkowski and a new type of domain wall solution to the Bogomol'nyi equations. We relate these vacua to type IIB D-branes.
We explicitly construct $N=10$ Chern-Simons gaged supergravity in three dimensions with non-semisimple gauge group $SO(5)\ltimes \mathbf{T}^{10}$. The gauge group is embedded in $E_{6(-14)}$ which is the isometry group of the 32-dimensional scalar manifold $E_{6(-14)}/SO(10)\times U(1)$. The resulting theory is on-shell equivalent to $SO(5)$ Yang-Mills gauged supergravity coming from dimensional reduction on $S^1$ of $SO(5)$ $N=5$ gauged supergravity in four dimensions. We discuss the spectrum of the corresponding reduction. The $SO(5)\ltimes \mathbf{T}^{10}$ gauged supergravity, describing th…
We determine the gauge symmetries of all p-forms in maximal three-dimensional gauged supergravity by requiring invariance of the Lagrangian. It is shown that in a particular ungauged limit these symmetries are in precise correspondence to those predicted by the very-extended Kac-Moody algebra E11. We demonstrate that whereas in the ungauged limit the bosonic gauge algebra closes off-shell, the closure is only on-shell in the full gauged theory. This underlines the importance of dynamics for understanding the Kac-Moody origin of the symmetries of gauged supergravity.
We identify the space of symplectic deformations of maximal gauged supergravity theories. Coordinates of such space parametrize inequivalent supergravity models with the same gauge group. We apply our procedure to the SO(8) gauging, extending recent analyses. We also study other interesting cases, including Cremmer-Scherk-Schwarz models and gaugings of groups contained in SL(8,R) and in SU*(8).
We construct a consistent reduction ansatz of eleven-dimensional supergravity to $N=2$ $SO(4)$ seven-dimensional gauged supergravity with topological mass term for the three-form field. The ansatz is obtained from a truncation of the $S^4$ reduction giving rise to the maximal $N=4$ $SO(5)$ gauged supergravity. Therefore, the consistency is guaranteed by the consistency of the $S^4$ reduction. Unlike the gauged supergravity without topological mass having a half-supersymmetric domain wall vacuum, the resulting 7D gauged supergravity theory admits a maximally supersymmetric $AdS_7$ critical poin…
We obtain a new gauged D=6, N=(1,1) pure supergravity by a generalised consistent Kaluza-Klein reduction of M-theory on K3 \times R. The reduction requires a conspiratory gauging of both the Cremmer-Julia type global (rigid) symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion. The gauged supergravity is different from the Romans D=6 gauged supergravity in that the four vector fields in our new theory are all abelian. We show that it admits a supersymmetric (Minkowski)_4\times S^2 vacuum, which can be lifted to D=11 where it becomes the near-horizon geometry …
We consider gauged five dimensional supergravity with boundaries and vector multiplets in the bulk. We analyse the zero modes of the BPS configurations preserving N=1 supergravity at low energy. We find the 4d low energy effective action involving the moduli associated to the BPS zero modes. In particular, we derive the Kähler potential on the moduli space corresponding to the low energy 4d N=1 effective action.
We construct the complete and explicit non-linear Kaluza-Klein ansatz for deriving the bosonic sector of N=4 SU(2)\times U(1) gauged five-dimensional supergravity from the reduction of type IIB supergravity on S^5. This provides the first complete example of such an S^5 reduction that includes non-abelian gauge fields, and it allows any bosonic solution of the five-dimensional N=4 gauged theory to be embedded in D=10.
We present a new anomaly-free gauged N=1 supergravity model in six dimensions. The gauge group is E_7xG_2xU(1)_R, with all hyperinos transforming in the product representation {56,14). The theory admits monopole compactifications to R^4xS^2, leading to D=4 effective theories with broken supersymmetry and massless fermions.
Five nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group $SO(8)\times SO(8)$ by restricting the potential to a submanifold of the space of $SU(3)\subset(SO(8)\times SO(8))_{\rm diag}$ singlets. The construction presented here uses the embedding of $E_{7(+7)}\subset E_{8(+8)}$ to lift the analysis of N=8, D=4 supergravity performed by N. Warner to N=16, D=3, and hence, these stationary points correspond to some of the known extrema of gauged N=8, D=4 supergravity.
We study a solution generating technique in supergravity which can be viewed as a generalised version of U-duality, taking solutions of type IIA supergravity on a 6-sphere with RR flux to new solutions of 11-dimensional supergravity. The new solutions are characterised by an underlying 6-algebra structure. Our construction provides an 11-dimensional uplift of four-dimensional ISO(7) gauged supergravity, using $E_7$ exceptional geometry techniques. We focus on an example where we start with the D2 solution in type IIA supergravity and construct a new $\tfrac12$-BPS 11-dimensional solution.
In this thesis we study maximally supersymmetric solutions of gauged supergravity theories, with special focus on anti-de Sitter solutions. The latter are relevant in the context of the AdS/CFT correspondence. In the first part we classify all maximally supersymmetric solutions of all gauged or deformed supergravity theories in $D \geq 3$ space-time dimensions. In the second part we exclusively study maximally supersymmetric AdS$_D$ solutions of gauged supergravities in dimensions $D \geq 4$. We discuss the structure of the allowed gauge groups as well as possible supersymmetry preserving defo…
We obtain holographic constraints on the microscopic degeneracies of black holes by computing the exact macroscopic quantum entropy using localization, including the effects of string worldsheet instantons in the supergravity effective action. For $\frac14$-BPS black holes in type II string theory on $K3 \times T^{2}$, the constraints can be explicitly checked against expressions for the microscopic BPS counting functions that are known in terms of certain mock modular forms. We find that the effect of including the infinite sum over instantons in the holomorphic prepotential of the supergravi…
We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a non-trivial embedding of the special Lagrangian three-cycle wrapped by the D6-branes in the lower dimensional supergravity. There are constraints that neatly reduce the general ansatz to a six functions one. Within this approach, the Hitchin system and the flop transformation are nicely realized in eight dimensional gauged supergravity.
We consider giant graviton probes of 11-dimensional supergravity solutions which are lifts of arbitrary solutions of 4-dimensional U(1)^4 and 7-dimensional U(1)^2 gauged supergravities. We show that the structure of the lift ansatze is sufficient to explicitly find a solution for the embedding and motion of the M5- or M2-brane in the internal space. The brane probe action then reduces to that of a massive charged particle in the gauged supergravity, demonstrating that probing the gauged supergravity with such particles is equivalent to the more involved 11-dimensional brane probe calculation. …
We construct solutions of four-dimensional $N=2$ gauged supergravity coupled to vector multiplets which are holographically dual to superconformal line defects. For the gauged STU and the $SU(1,n)/U(1)\times SU(n)$ coset models, we use the solutions to calculate holographic observables such as the expectation value of the defect and one-point functions in the presence of the defect.
We review on a recent construction of the on-shell supersymmetric brane action for the codimension-two branes with nonzero tension in the flux compactification of a 6D chiral gauged supergravity. On dimesionally reducing on 4D gauged supergravity for a new supersymmetric unwarped background with conical branes, we consider the modulus stabilization for determining the soft masses of the scalars localized on the branes and show that the bulk U(1)_R provides a new mechanism for mediating the SUSY breaking.
We obtain the general solution for non-extremal 3-charge dilatonic rotating black holes in the U(1)^3 gauged five-dimensional N=2 supergravity coupled to two vector multiplets, in the case where the two rotation parameters are set equal. These solutions encompass all the previously-known extremal solutions, and, by setting the three charges equal, the recently-obtained non-extremal solutions of N=2 gauged five-dimensional pure supergravity.
The low-energy effective theories describing string compactifications in the presence of fluxes are so-called gauged supergravities: deformations of the standard abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.
We show how to expand the Lunin-Maldacena solution to the full bosonic sector of gauged $\mathcal N=2$ supergravity. In particular, we construct a consistent truncation of IIB supergravity on a $β$-deformed $\mathrm{AdS}_5\times S^5$ background retaining a dynamical metric and graviphoton in five dimensions. We comment on the relation between this solution and similar constructions on Sasaki-Einstein manifolds, as well as the possibility of further consistent truncations which generalize the Lunin-Maldacena solution.
Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed qua…
Domain wall and electrovac solutions of gauged N=4 D=4 supergravity, with gauge group SU(2) or SU(2)xSU(2), are interpreted as supersymmetric Kaluza-Klein vacua of N=1 D=10 supergravity. These vacua are shown to be the near-horizon geometries of certain intersecting brane solutions.
We study the SO(4)-symmetric solution of the five-dimensional SU(2) x U(1) gauged N=4 supergravity theory obtained in [hep-th/0101202]. This solution contains purely magnetic non-Abelian and electric Abelian fields. It can be interpreted as a reduction of seven-dimensional gauged supergravity on a torus, which comes from type IIB supergravity on S^3. We also show how to obtain that solution from six-dimensional Romans' theory on a circle. We then up-lift the solution to massless type IIA supergravity. The dual gauge field theory is twisted and is defined on the worldvolume of a NS-fivebrane wr…
In this note we discuss the classification of duality orbits of N = 8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings and the scalar potential are parameter dependent. We also comment on the possible M-theory uplift and on the meaning of the parameter for the dual gauge theories.
We study, in the context of five dimensional N=2 gauged supergravity with vector and hypermultiplets, curved domain wall solutions with worldvolumes given by four dimensional Einstein manifolds. For a choice of the projection condition on the Killing spinors of the BPS solutions, first order differential equations governing the flow of the scalars are derived. With these equations, we analyze the equations of motion and determine conditions under which gauged supergravity theories may admit Einstein domain wall solutions.
We find a family of complete non-linear Kaluza-Kein reduction ansatze from type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic sector. The reduction is over a sphere $S^2$ and a Riemann surface $Σ$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $Σ$. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB supergravity that depend on these same functions $\mathcal{A}_{\pm}$.
We study the supergravity duals of supersymmetric theories arising in the world-volume of D6 branes wrapping holomorphic two-cycles and special Lagrangian three-cycles within the framework of eight dimensional gauged supergravity. When uplifted to 11d, our solutions represent M-theory on the background of, respectively, the small resolution of the conifold and a manifold with G_2 holonomy. We further discuss on the flop and other possible geometrical transitions and its implications.
Through the construction of a complete non-linear Kaluza-Klein reduction ansatz from type IIB supergravity to Romans' F(4) gauged supergravity, we identify a recently discovered supersymmetric AdS_6 solution as the IIB uplift of the supersymmetric vacuum of Romans' theory. We present new IIB uplifts of a number of known solutions of Romans' theory and comment on supersymmetry in higher-dimensions where it is expected.
Janus solutions are constructed in $d=3$, ${\cal N}=8$ gauged supergravity. We find explicit half-BPS solutions where two scalars in the $SO(8,1)/SO(8)$ coset have a nontrivial profile. These solutions correspond on the CFT side to an interface with a position-dependent expectation value for a relevant operator and a source which jumps across the interface for a marginal operator.
This is a slightly expanded version of my talk at Future Perspectives in Theoretical Physics and Cosmology, Stephen Hawking's 60th Birthday Worshop. I describe some of the issues that were important in gauged supergravity in the 1980's and how these, and related issues have once again become important in the study of holographic field theories.
States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.
In this paper, we continue the study of Janus and RG-flow interfaces in three dimensional supergravity continuing the work presented in [1]. We consider ${\cal N}=8$ gauged supergravity theories which have a ${\cal N}=(4,4)$ $AdS_3$ vacuum with $D^1(2,1;α) \times D^1(2,1;α)$ symmetry for general $α$. We derive the BPS flow equations and find numerical solutions. Some holographic quantities such as the entanglement entropy are calculated.
We study supersymmetric Janus solutions of dyonic $ISO(7)$-gauged $\mathcal{N}$ = 8 supergravity. We mostly find Janus solutions flowing to 3d $\mathcal{N}$ = 8 SYM phase which is the worldvolume theory on D2-branes and non-conformal. There are also solutions flowing from the critical points which are dual to 3d SCFTs from deformations of the D2-brane theory.
In this paper we study the holographic dual to a-maximization in five-dimensional N = 2 gauged supergravity. In particular, we apply the procedure described by Tachikawa to specific examples consisting of holographic duals to gauge theories arising as the IR limit of N M5-branes wrapping a Riemann surface. A key element of this analysis is a consistent truncation of seven-dimensional N = 4 SO(5) gauged supergravity reduced on a Riemann surface. We demonstrate the consistency of this truncation and match to a sector of five-dimensional matter-coupled N = 2 gauged supergravity. We determine the …
We study exact renormalization group (RG) in O(4) gauged supergravity using the effective average action formalism. The nonperturbative RG equations for cosmological and newtonian coupling constants are found. It is shown the existence of (nonstable) fixed point of these equations. The solution of RG equation for newtonian coupling constant is qualitatively the same as in Einstein gravity(i.e. it is growing at large distances).
We systematically study all supersymmetric solutions of six-dimensional (2,0) supergravity with a null isometry. In particular, every such solution with at least four real supersymmetries is also a supersymmetric solution of a (1,0) theory preserving the same absolute amount of supersymmetry. This implies that no genuinely new solutions of this type can be found in this framework. The microstate geometries associated to supersymmetric black holes within Mathur's proposal are generically supersymmetric solutions of six-dimensional supergravity. A direct consequence of our result is that supersy…
We discuss a possibility of restricting parameters in $\mathcal{N}=2$ supergravity based on axion observations. We derive conditions that prepotential and gauge couplings should satisfy. Such conditions not only allow us to constrain the theory but also provide the lower bound of $\mathcal{N}=2\rightarrow\mathcal{N}=1$ breaking scale.
We propose a novel realization of spontaneous supersymmetry breaking in de Sitter vacuum by F- and D-terms in $N=1$ four-dimensional supergravity coupled to a chiral superfield with $SU(1,1)/U(1)$ target space. Our construction features gauged $U(1)_R$ symmetry rotating the chiral scalar field by a phase. Both SUSY and R-symmetry can be spontaneously broken, and for two particular parameter choices we obtain no-scale supergravity with positive tunable cosmological constant.
