Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality

Abstract

According to more recent AdS/CFT interpretation \cite{Karch:2015rpa}, in which varying cosmological constant $\Lambda$ in the bulk corresponds to varying the curvature radius governing the space on which the field theory resides, we study the criticality of thermodynamic curvatures for thermal boundary conformal field theories (CFT) that are dual to $d$-dimensional charged anti-de Sitter (AdS) black holes, embedded in $D$-dimensional M-theory/superstring inspired models having $Ad{S}_d\times {\mathbb{S}}^{d+k}$ spacetime with $D=2d+k$. Analogous with criticality features acquired for charged AdS black holes in the bulk \cite{HosseiniMansoori:2020jrx}, the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ of the boundary CFT has critical exponents 2 and 1, respectively. In this respect, the universal amplitude of $R_N{t}^2$ is $\frac{1}{2}$ and $K_{N}t$ is $-\frac{1}{2}$ when $t\to 0^{-}$, whereas $R_N{t}^2\approx \frac{1}{8}$ and $K_{N}t\approx \frac{1}{4}$ in the limit $t\to 0^{+}$ in which $t=T/T_c-1$ is the temperature parameter with the critical temperature, $T_c$. Interestingly, these critical amplitudes are independent of the number of thermal CFT dimensions and are remarkably similar to one given for higher dimensional charged AdS black holes in the bulk.

arXiv comment21 pages, 5 figures, 2 tables

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• Holographic CFT Phase Transitions and Criticality for Charged AdS Black Holes
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• Thermodynamics of Kerr-AdS black holes in the restricted phase space
• Black hole thermodynamics is extensive with variable Newton constant
• Weak Cosmic Censorship and Weak Gravity Conjectures in CFT Thermodynamics
• QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes
• Thermodynamics and phase transition in central charge criticality of charged Gauss-Bonnet AdS black holes
• Thermodynamic geometry of pure Lovelock black holes
• Restricted Phase Space Thermodynamics of NED-AdS Black Holes
• A varying gravitational constant map in asymptotically AdS black hole thermodynamics