Thermodynamic Geometry of black hole in the deformed Horava-Lifshitz gravity

We investigate the thermodynamic geometry and phase transition of Kehagias-Sfetsos black hole in the deformed Horava-Lifshitz gravity with coupling constant $\lambda=1$. The phase transition in black hole thermodynamics is thought to be associated with the divergence of the capacities. And the structures of these divergent points are studied. We also find that the thermodynamic curvature produced by the Ruppeiner metric is positive definite for all $r_+ > r_-$ and is divergence at $\eta_2=0$ corresponded to the divergent points of $C_{\Phi}$ and $C_T$. These results suggest that the microstructure of the black hole has an effective repulsive interaction, which is very similar to the ideal gas of fermions. These may shine some light on the microstructure of the black hole.Comment: 5 pages, 3 figure

Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory

We consider the non-relativistic superconformal U(N) X U(N) Chern-Simons theory with level (k,-k) possessing fourteen supersymmetries. We obtain an exact four-point scattering amplitude of the theory to all orders in 1/N and 1/k and prove that the scattering amplitude becomes trivial when k=1 and 2. We confirm this amplitude to one-loop order by using an explicit field theoretic computation and show that the beta function for the contact interaction vanishes to the one-loop order, which is consistent with the quantum conformal invariance of the underlying theory.Comment: 16 page

Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Ho\v{r}ava-Lifshitz gravity at the Lifshitz point $z=3$. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits the second order phase transition within the {\it physical region} of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.Comment: Minor corrections, refs. added, to appear in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:1111.0973 by other author

Non-relativistic metrics with extremal limits

We present solutions of type IIB supergravity with z=2 Schrodinger asymptotics that admit an extremal limit, i.e. the black hole horizon has a double zero. These solutions are obtained as TsT transformations of the charged planar black hole in AdS_5 \times S^5. Unlike the uncharged solution, the Ramond-Ramond two-form is turned on. We study the thermodynamic properties of these new solutions, and we show that the ratio of shear viscosity to entropy density is 1/4\pi even in the extremal limit. We also consider the TsT-transformed soliton and show that, for a special radius of the compact circle, there is a confinement-deconfinement phase transition at zero temperature between the soliton and black hole phases.Comment: 23 pages, references and clarifications added, typos corrected, restriction in phase transition due to equation 6.5 emphasized; published versio

On the Renormalizability of Horava-Lifshitz-type Gravities

In this note, we discuss the renormalizability of Horava-Lifshitz-type gravity theories. Using the fact that Horava-Lifshitz gravity is very closely related to the stochastic quantization of topologically massive gravity, we show that the renormalizability of HL gravity only depends on the renormalizability of topologically massive gravity. This is a consequence of the BRST and time-reversal symmetries pertinent to theories satisfying the detailed balance condition.Comment: 13 pages, references added, typos fixe

Janus Black Holes

In this paper Janus black holes in AdS3 are considered. These are static solutions of an Einstein-scalar system with broken translation symmetry along the horizon. These solutions are dual to interface conformal field theories at finite temperature. An approximate solution is first constructed using perturbation theory around a planar BTZ black hole. Numerical and exact solutions valid for all sets of parameters are then found and compared. Using the exact solution the thermodynamics of the system is analyzed. The entropy associated with the Janus black hole is calculated and it is found that the entropy of the black Janus is the sum of the undeformed black hole entropy and the entanglement entropy associated with the defect.Comment: 28 pages, 2 figures, reference adde

Electrodynamics a la Horava

We study an electrodynamics consistent with anisotropic transformations of space-time with an arbitrary dynamic exponent $z$. The equations of motion and conserved quantities are explicitly obtained. We show that the propagator of this theory can be regarded as a quantum correction to the usual propagator. Moreover we obtain that both the momentum and angular momentum are not modified, but their conservation laws do change. We also show that in this theory the speed of light and the electric charge are modified with $z$. The magnetic monopole in this electrodynamics and its duality transformations are also investigated. For that we found that there exists a dual electrodynamics, with higher derivatives in the electric field, invariant under the same anisotropic transformations.Comment: 14 pages, no figures, version to appears in Mod. Phys. Lett.

AdS spacetimes from wrapped D3-branes

We derive a geometrical characterisation of a large class of AdS_3 and AdS_2 supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux using G-structures. These are obtained as special cases of a class of supersymmetric spacetimes with an $\mathbb{R}^{1,1}$ or $\mathbb{R}$ (time) factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles, respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show how two explicit AdS solutions, previously constructed in gauged supergravity, satisfy our more general G-structure conditions. For each explicit solution we also derive a special holonomy metric which, although singular, has an appropriate calibrated cycle. After analytic continuation, some of the classes of AdS spacetimes give rise to known classes of BPS bubble solutions with $\mathbb{R}\times SO(4)\times SO(4)$, $\mathbb{R}\times SO(4)\times U(1)$, and $\mathbb{R}\times SO(4)$ symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with $\mathbb{R}\times SU(2)$ symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-branes wrapped on associative three-cycles.Comment: 1+30 pages; v2, references added; v3, typos corrected, reference adde

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schr\"odinger type via a z=2 QCP.Comment: references added. minor changes. version published in JHE