Beyond LLM in M-theory

The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent Killing directions when a general Killing spinor ansatz is considered. Here we show that these directions always commute, identify when the Killing spinors are charged, and show that both their inner product and resulting geometry are governed by two fundamental constants. In particular, setting one constant to zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat spacetime is recovered when both these constants are zero. Furthermore, when the constants are equal, the spacetime is either LLM, or it corresponds to the Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde

Semiclassical strings in marginally deformed toric AdS/CFT

We study string solutions in the beta-deformed Sasaki-Einstein gauge/gravity dualities. We find that the BPS point-like strings move in the submanifolds where the two U(1) circles shrink to zero size. In the corresponding T^3 fibration description, the strings live on the edges of the polyhedron, where the T^3 fibration degenerates to T^1. Moreover, we find that for each deformed Sasaki-Einstein manifold the BPS string solutions exist only for particular values of the deformation parameter. Our results imply that in the dual field theory the corresponding BPS operators exist only for these particular values of the deformation parameter we find. We also examine the non-BPS strings, derive their dispersion relations and compare them with the undeformed ones. Finally, we comment on the range of the validity of our solutions and their dependence on the deformation parameter.Comment: 29 pages, 9 figure

A new phase for the anisotropic N=4 super Yang-Mills plasma

Black hole solutions of type IIB supergravity have been previously constructed that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. The zero temperature limit of these black holes approach a Lifshitz-like scaling solution in the infrared. We show that these black holes become unstable at low temperature and we construct a new class of black hole solutions which are thermodynamically preferred. The phase transition is third order and incorporates a spontaneous breaking of the $SO(6)$ global symmetry down to $SO(4)\times SO(2)$. The critical exponents for the phase transition are given by $(\alpha,\beta,\gamma,\delta)=(-1,1,1,2)$ which differ from the standard mean-field exponents usually seen in holography. At low temperatures the black holes approach a novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation. We show that the new ground states are thermal insulators in the direction of the anisotropy.Comment: 26 pages, 5 figure. Minor changes; version published in JHE

Fermions and Type IIB Supergravity On Squashed Sasaki-Einstein Manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U(1) subgroup of the $R$-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.Comment: 43 pages, 2 figures, PDFLaTeX; v2: added references, typos corrected, minor change

Rigidity of SU(2,2|2)-symmetric solutions in Type IIB

We investigate the existence of half-BPS solutions in Type IIB supergravity which are invariant under the superalgebra SU(2,2|2) realized on either AdS_5 x S^2 x S^1 or AdS_5 x S^3 warped over a Riemann surface \Sigma with boundary. We prove that, in both cases, the only solution is AdS_5 x S^5 itself. We argue that this result provides evidence for the non-existence of fully back-reacted intersecting D3/D7 branes with either AdS_5 x S^2 x S^1 x \Sigma or AdS_5 x S^3 x \Sigma near-horizon limits.Comment: 55 page

Quantum Criticality and Holographic Superconductors in M-theory

We present a consistent Kaluza-Klein truncation of D=11 supergravity on an arbitrary seven-dimensional Sasaki-Einstein space (SE_7) to a D=4 theory containing a metric, a gauge-field, a complex scalar field and a real scalar field. We use this D=4 theory to construct various black hole solutions that describe the thermodynamics of the d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions. We show that these CFTs have a rich phase diagram, including holographic superconductivity with, generically, broken parity and time reversal invariance. At zero temperature the superconducting solutions are charged domain walls with a universal emergent conformal symmetry in the far infrared.Comment: 52 pages, 16 figures, 3 appendices; minor changes, version to be published in JHE

Four-Dimensional SCFTs from M5-Branes

We engineer a large new set of four-dimensional N=1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS_5 M-theory backgrounds which describe these fixed points at large N, and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in arXiv:1112:5487.Comment: 45 pages, 11 figure

Toric geometry and the dual of c-extremization

We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface Σg, with an arbitrary partial topological twist for the global U(1) symmetries. This constitutes a rich, infinite class of two-dimensional (0, 2) theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and R-charges of BPS baryonic operators of the dual AdS3 solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the Yp,q and Xp,q 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using c-extremization, for arbitrary twist over Σg. We furthermore conjecture that the trial central charge Open image in new window , which we define in gravity, matches the field theory trial c-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions

Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics

We construct asymptotically AdS_5 solutions to 5-dimensional Einstein-Maxwell theory with Chern-Simons term which are dual to 4-dimensional gauge theories, including N=4 SYM theory, in the presence of a constant background magnetic field B and a uniform electric charge density \rho. For the solutions corresponding to supersymmetric gauge theories, we find numerically that a small magnetic field causes a drastic decrease in the entropy at low temperatures. The near-horizon AdS_2 \times R^3 geometry of the purely electrically charged brane thus appears to be unstable under the addition of a small magnetic field. Based on this observation, we propose a formulation of the third law of thermodynamics (or Nernst theorem) that can be applied to black holes in the AdS/CFT context. We also find interesting behavior for smaller, non-supersymmetric, values of the Chern-Simons coupling k. For k=1 we exhibit exact solutions corresponding to warped AdS_3 black holes, and show that these can be connected to asymptotically AdS_5 spacetime. For k\leq 1 the entropy appears to go to a finite value at extremality, but the solutions still exhibit a mild singularity at strictly zero temperature. In addition to our numerics, we carry out a complete perturbative analysis valid to order B^2, and find that this corroborates our numerical results insofar as they overlap.Comment: 45 pages v2: added note about subsequent results found in arXiv:1003.130

Consistent supersymmetric Kaluza-Klein truncations with massive modes

We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki--Einstein space, and still consistent with N=2 supersymmetry. In the context of flux compactifications, the Sasaki--Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G_2 manifold leading to an N=1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N=8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.Comment: 33 pages. v2: Added section on skew-whiffed solutions and some brief comments on holographic superconductors. v3: typos corrected, version to be published in JHE