Holographic CFT Phase Transitions and Criticality for Einstein-Maxwell-Power-Yang-Mills AdS Black Holes

Abstract

We present a comprehensive study of the thermodynamic phase structure for Anti-de Sitter black holes in Einstein-Maxwell-power-Yang-Mills gravity, reformulated through holographic duality as an ensemble problem in the dual conformal field theory (CFT). By deriving an extended first law where the central charge \(C\) is a thermodynamic variable, we systematically explore both canonical and mixed ensembles. In the canonical ensemble with fixed charges, we identify a van der Waals-like phase transition between small and large black holes, marked by a characteristic swallowtail structure and coexistence curves with a negative slope. In contrast, within the mixed ensemble of fixed electric potential, the system exhibits a Hawking-Page transition between confined and deconfined phases of the boundary CFT. Our key finding is the suppressive role of the non-Abelian Yang-Mills charge \(\tilde{q}\): increasing \(\tilde{q}\) lowers both the minimum and the Hawking-Page transition temperatures, significantly narrowing the stability window of the confined phase. These results, supported by detailed numerical analysis, reveal a rich, ensemble-dependent phase landscape and establish the non-linear Yang-Mills sector as a critical controller of confinement physics in strongly coupled holographic systems.

Figures (7)

• Figure 1: Heat Capacity $\tilde{\mathcal{C}}$ against $S$, with R=1 , $\gamma=0.6$, and (a) $\tilde{q}=1.41820$, $C=2.5$ (b) $\tilde{Q}=1$, $C=2.5$ (c) $\tilde{q}=1.41820$, $\tilde{Q}=1$
• Figure 2: (a) Temperature $\tilde{T}$ vs. entropy $S$ (b) Free energy $\tilde{F}$ vs. temperature $\tilde{T}$ plot with R=1 , $\gamma=0.6$, $\tilde{q}=1.41820$ and, C=2.5 . The red dot marks the critical point.
• Figure 3: (a) Temperature $\tilde{T}$ vs. entropy $S$ (b) Free energy $\tilde{F}$ vs. temperature $\tilde{T}$ plot with R=1 , $\gamma=0.6$$\tilde{Q}=1$ and, C=2.5 . The red dot marks the critical point.
• Figure 4: (a) Temperature $\tilde{T}$ vs. entropy $S$ (b) Free energy $\tilde{F}$ vs. temperature $\tilde{T}$ plot with R=1 , $\gamma=0.6$$\tilde{q}=1.41820$, and, $\tilde{Q}=1$ . The red dot marks the critical point.
• Figure 5: Coexistence lines for the fixed $(\tilde{q},\tilde{Q}, \mathcal{V}, C)$ ensemble. Low-entropy and high-entropy coexistence curve for CFT thermal states on (a) $\tilde{Q}- \tilde{T}$ and (b),(c)$\tilde{q}-\tilde{T}$ phase diagram. The parameters used here are (a) $R = 1, C=1, \gamma=0.6$, (b) $R = 1, \tilde{Q}=1, \gamma=0.6$, and (c) $R = 1, C=2.5, \gamma=0.6$. For each value of (a) $q$ , (b) $C$, and (c) $\tilde{Q}$, the coexistence line represents a line of first-order phase transitions between low-entropy states (to the left of the line) and high-entropy states (to the right), and the line ends at a critical point where a second-order phase transition occurs at (a) $\tilde{Q}=\tilde{Q}_{c}$ and $\tilde{T}=\tilde{T}_{c}$ , (b), (c) $\tilde{q}=\tilde{q}_{c}$ and $\tilde{T}=\tilde{T}_{c}$.