Ensemble Dependent Holographic Phase Transitions in 4$D$ Dyonic AdS Black Holes

TL;DR

This paper explores the complex phase structure of 4D dyonic AdS black holes within holography, revealing how various thermodynamic ensembles and variables influence phase transitions like Van der Waals, superfluid, and Davies criticality.

Contribution

It systematically analyzes all sixteen thermodynamic ensembles of dyonic AdS black holes, uncovering new phase behaviors influenced by electric/magnetic charges and CFT variables.

Findings

Identification of Van der Waals, superfluid, and Davies transitions in specific ensembles.

Discovery of a confined/deconfined transition in a particular ensemble.

Highlighting the impact of dyonic charges and CFT variables on phase structure.

Abstract

This work studies the holographic thermodynamics of $4D$ dyonic Anti--de Sitter black holes within the AdS/CFT correspondence. By allowing variations of the cosmological constant $\Lambda$ and Newton's constant $G_N$, the gravitational thermodynamics is extended to include the CFT central charge $C$ and its conjugate chemical potential $\mu$, together with the standard thermodynamic pair $(T,S)$. A further conjugate pair $(p,\mathcal{V})$, interpreted as the CFT pressure and volume, is also introduced. The presence of both electric and magnetic charges, described by $(\tilde{\Phi}_e,\tilde{Q}_e)$ and $(\tilde{\Phi}_m,\tilde{Q}_m)$, leads to a significantly enriched phase structure. A systematic analysis of all sixteen thermodynamic ensembles reveals a strong dependence of phase behavior on ensemble choice. In the ensembles $(\tilde{Q}_m,\tilde{\Phi}_e,\mathcal{V},C)$ and $(\tilde{Q}_e,\tilde{\Phi}_m,\mathcal{V},C)$, the system exhibits Van der Waals transitions, superfluid $\lambda$ transitions, and Davies criticality, while the ensemble $(\tilde{Q}_m,\tilde{Q}_e,\mathcal{V},C)$ supports similar transitions except for the Davies transitions. When the chemical potential $\mu$ is fixed, only Davies--type transitions occur. Ensembles involving the CFT pressure $p$ show no critical behavior, although Davies transitions persist. Notably, the ensemble $(\tilde{\Phi}_m,\tilde{\Phi}_e,\mathcal{V},C)$ uniquely displays a confined/deconfined transition alongside Davies criticality. These results highlight the crucial role of dyonic charges and CFT variables in shaping holographic phase transitions.