Holographic CFT Phase Transitions and Criticality for Charged AdS Black Holes

TL;DR

This paper explores the holographic dual of charged AdS black holes' thermodynamics, revealing phase transitions and critical phenomena in the dual CFT, and clarifying the absence of Van der Waals-like behavior.

Contribution

It introduces a detailed holographic analysis of extended thermodynamics for charged AdS black holes, highlighting new phase transitions and the role of various thermodynamic variables in the dual CFT.

Findings

Discovery of a zeroth-order phase transition at fixed chemical potential.

Identification of critical phenomena in certain thermodynamic ensembles.

Absence of Van der Waals criticality in fixed pressure ensembles.

Abstract

We study the hololgraphic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton's constant. In the dual CFT this corresponds to including the central charge $C$ and its chemical potential $\mu$ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy $(T,S)$, electric potential vs. charge $(\tilde \Phi, \tilde Q)$ and field theory pressure vs. volume $(p,{\cal V})$. For the (grand) canonical ensembles at fixed $(\tilde Q, {\cal V}, C), (\tilde \Phi, {\cal V},C)$ and $(\tilde Q, {\cal V}, \mu)$ we show the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed $(\tilde Q, \mathcal V, \mu)$ we find a new zeroth-order phase transition between a high- and low-entropy phase at some $\mu$-dependent temperature. Finally, we point out there is no critical behaviour in the fixed $p$ ensembles, i.e. there is no $p - \cal V$ criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid.