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

SYK/AdS duality with Yang-Baxter deformations

In this paper, based on the notion of SYK/AdS duality we explore the effects of Yang-Baxter (YB) deformations on the SYK spectrum at strong coupling. In the first part of our analysis, we explore the consequences of YB deformations through the Kaluza-Klein (KK) reduction on $(AdS_2)_{\eta}\times (S^1)/Z_2$. It turns out that the YB effects (on the SYK spectrum) starts showing off at \textit{quadratic} order in $1/J$ expansion. For the rest of the analysis, we provide an interpretation for the YB deformations in terms of bi-local/collective field excitations of the SYK model. Using large $N$ techniques, we evaluate the effective action upto quadratic order in the fluctuations and estimate $1/J^2$ corrections to the correlation function at strong coupling.Comment: Revised version, To Appear in JHE