We present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance. They are expected to describe a class of D3-D7 systems and their finite temperature generalizations are straightforward. We show that there exist solutions that interpolate between these anisotropic solutions in the IR and the standard AdS 5 solutions in the UV. This predicts anisotropic RG flows from familiar isotropic fixed points to anisotropic ones. In our case, these RG flows are triggered by a non-zero theta-angle in Yang-Mills theories that linearly depends on one of the spatial coordinates. We study the perturbations around these backgrounds and discuss the possibility of instability. We also holographically compute their thermal entropies, viscosities, and entanglement entropies.

We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS 2 =CFT 1 . As an explicit example, we study near extremal Banados-Teitelboim-Zanelli black holes and derive this claim from AdS 3 =CFT 2 . We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.

We use the holographic proposal for calculating entanglement entropies to determine the boundary entropy of defects in strongly coupled two-dimensional conformal field theories. We study several examples including the Janus solution and show that the boundary entropy extracted from the entanglement entropy as well as its more conventional definition via the free energy agree with each other. Maybe somewhat surprisingly we find that, unlike in the case of a conformal field theory with boundary, the entanglement entropy for a generic region in a theory with defect carries detailed information about the microscopic details of the theory. We also argue that the g-theorem for the boundary entropy is closely related to the strong subadditivity of the entanglement entropy. 1

We study the Schwinger-Dyson equations of a fermionic planar matrix quantum mechanics [or tensor and Sachdev-Ye-Kitaev (SYK) models] at leading melonic order. We find two solutions describing a high entropy, SYK black-hole-like phase and a low entropy one with trivial IR behavior. There is a line of first order phase transitions that terminates at a new critical point. Critical exponents are nonmean field and differ on the two sides of the transition. Interesting phenomena are also found in unstable and stable bosonic models, including Kazakov critical points and inconsistency of SYK-like solutions of the IR limit.

We study the asymptotic Virasoro symmetry which acts on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections, following the recently proposed Kerr/CFT correspondence. We demonstrate that its central charge correctly reproduces the entropy formula of Iyer-Wald, once the boundary terms in the symplectic structure are carefully chosen. Downloaded fromhigher derivative corrections were discussed in 10).* ) The higher-derivative contribution to the central charge of the asymptotic Virasoro algebra of AdS 3 was studied in 38) and 39). The former treated the diffeomorphism-invariant Lagrangian density, but used the field redefinition specific to three dimensions which rewrites arbitrary such Lagrangians to the Einstein-Hilbert term with scalar fields with higher-derivative interactions. The latter paper dealt the topologically massive gravity 40) in the canonical ADM formalism, more directly following the approach taken by Brown-Henneaux. 3) It would be instructive to redo their analyses using the covariant phase space method. * * ) The relationship between cohomological methods 15)-18) and the closely related covariant methods based on the linear equations of motion 41)-43) and covariant symplectic methods in first order theories 44), 45) are detailed in 18). at Ernst Mayr Library of the Museum Comp Zoology, Harvard University on July 18, 2015 http://ptp.oxfordjournals.org/ Downloaded from * )Here a corresponds to a trivial cocycle and can be absorbed to a redefinition of H 0 . One can determine a natural definition of the angular momentum H 0 = H ∂ ϕ by performing such change so that a becomes the standard −1, but we do not pursue this direction in this paper.at