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The gravitational dual of c-extremization for a class of (0, 2) two-dimensional theories obtained by twisted compactifications of D3-brane gauge theories living at a toric Calabi-Yau three-fold has been recently proposed. The equivalence of this construction with c-extremization has been checked in various examples and holds also off-shell. In this note we prove that such equivalence holds for an arbitrary toric Calabi-Yau. We do it by generalizing the proof of the equivalence between a-maximization and volume minimization for four-dimensional toric quivers. By an explicit parameterization of the R-charges we map the trial right-moving central charge c r into the off-shell functional to be extremized in gravity. We also observe that the similar construction for M2-branes on ℂ 4 is equivalent to the ℐ-extremization principle that leads to the microscopic counting for the entropy of magnetically charged black holes in AdS 4 × S 7 . Also this equivalence holds off-shell

We find a family of AdS2×ℳ4 supersymmetric solutions of the six-dimensional F(4) gauged supergravity coupled to one vector multiplet that arises as a low energy description of massive type IIA supergravity on (warped) AdS6 × S4. ℳ4 is either a Kähler-Einstein manifold or a product of two Riemann surfaces with a constant curvature metric. These solutions correspond to the near-horizon region of a family of static magnetically charged black holes. In the case where ℳ4 is a product of Riemann surfaces, we successfully compare their entropy to a microscopic counting based on the recently computed topologically twisted index of the five-dimensional N = 1 USp(2N) theory with Nf fundamental flavors and an antisymmetric matter field. Furthermore, our results suggest that the near-horizon regions exhibit an attractor mechanism for the scalars in the matter coupled F(4) gauged supergravity, and we give a proposal for it.

In this note we show that the entropy of BPS, rotating, electrically charged AdS7 × S4 black holes can be obtained by an extremization principle involving a particular combination of anomaly coefficients of the six-dimensional N= (2 0) theory. This result extends our previous finding for BPS, rotating AdS5× S5 black holes.

Many three-dimensional N = 2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS4magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS2solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS5 × S5 can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for N= 4 super Yang-Mills.

We evaluate the topologically twisted index of a general four-dimensional N= 1 gauge theory in the “high-temperature” limit. The index is the partition function for N= 1 theories on S2× T2, with a partial topological twist along S2, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional N= (0 2) SCFTs obtained from the compactification on S2. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS5× SE5, where SE5 are five-dimensional Sasaki-Einstein spaces

We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.

We provide general formulae for the topologically twisted index of a general three-dimensional N ≥ 2 gauge theory with an M-theory or massive type IIA dual in the large N limit. The index is defined as the supersymmetric path integral of the theory on S2 × S1 in the presence of background magnetic fluxes for the R- and global symmetries and it is conjectured to reproduce the entropy of magnetically charged static BPS AdS4 black holes. For a class of theories with an M-theory dual, we show that the logarithm of the index scales indeed as N3/2 (and N5/3 in the massive type IIA case). We find an intriguing relation with the (apparently unrelated) large N limit of the partition function on S3. We also provide a universal formula for extracting the index from the large N partition function on S3 and its derivatives and point out its analogy with the attractor mechanism for AdS black holes.

This paper addresses a long standing problem, the counting of the microstates of supersymmetric asymptotically AdS black holes in terms of a holographically dual field theory. We focus on a class of asymptotically AdS4static black holes preserving two real supercharges which are dual to a topologically twisted deformation of the ABJM theory. We evaluate in the large N limit the topologically twisted index of the ABJM theory and we show that it correctly reproduces the entropy of the AdS4black holes. An extremization of the index with respect to a set of chemical potentials is required. We interpret it as the selection of the exact R-symmetry of the superconformal quantum mechanics describing the horizon of the black hole.

We find a new class of N = 2 massive IIA solutions whose internal spaces are S2 vibrations over S2 - S2. These solutions appear naturally as massive deformations of the type IIA reduction of Sasaki-Einstein manifolds in M-theory, including Q1;1;1 and Y p;k, and play a role in the AdS4/CFT3 correspondence. We use this example to initiate a systematic study of the parameter space of massive solutions with uxes. We dene and study the natural parameter space of the solutions, which is a certain dense subset of R3, whose boundaries correspond to orbifold or conifold singularities. On a codimension-one subset of the parameter space, where the Romans mass vanishes, it is possible to perform a lift to M-theory; extending earlier work, we produce a family Ap;q;r of Sasaki-Einstein manifolds with cohomogeneity one and SU(2) SU(2) U(1) isometry. We also propose a Chern-Simons theory describing the duals of the massless and massive solutions. © SISSA 2011.

We find infinite families of supersymmetric solutions of four dimensional, N = 2 gauged supergravity with Lifshitz, Schrödinger and also AdS symmetries. We focus on the canonical example of a single hypermultiplet and a single vector multiplet and find that the spectrum of solutions depends crucially on whether the gaugings are electric or magnetic but to a far milder extent on the strength of the gaugings. For purely electric or purely magnetic gaugings we generically find Lifshitz solutions, while for a mixed gauging we find Schrödinger and AdS solutions. For some of the gaugings the theory has a known lift to string/M-theory thus giving a higher dimensional embedding of our solutions. © 2011 SISSA.

Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in extAd extS4 ×mathbbCmathbbP3 { ext{Ad}}{{ ext{S}}_4} imes mathbb{C}{mathbb{P}^3} : one, previously known, with N = 1 mathcal{N} = 1 supersymmetry, and a new one with N = 2 mathcal{N} = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 mathcal{N} = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N. This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N.

We construct new families of interpolating two-parameter solutions of type IIB supergravity. These correspond to D3-D5 systems on non-compact six-dimensional manifolds which are T2 fibrations over Eguchi-Hanson and multi-center Taub-NUT spaces, respectively. One end of the interpolation corresponds to a solution with only D5 branes and vanishing NS three-form flux. A topology changing transition occurs at the other end, where the internal space becomes a direct product of the four-dimensional surface and the two-torus and the complexified NS-RR three-form flux becomes imaginary self-dual. Depending on the choice of the connections on the torus fibre, the interpolating family has either N = 2 or N = 1 supersymmetry. In the N = 2 case it can be shown that the solutions are regular. © SISSA 2010.

We construct three dimensional N = 1 Chern-Simons theories living on M2 branes probing Spin(7) cones. We consider Spin(7) manifolds obtained as quotients of Calabi-Yau four-folds by an anti-holomorphic involution, following a construction by Joyce. The corresponding Chern-Simons theories can be obtained from N = 2 theories by an orientifolding procedure. These theories are holographically dual to M theory solutions AdS4 × H, where the weak G2 manifold H is the base of the Spin(7) cone.