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

TL;DR

This paper demonstrates a universal critical behavior of thermodynamic geometries in boundary conformal field theories dual to charged AdS black holes, revealing dimension-independent critical amplitudes and exponents in the gauge/gravity duality framework.

Contribution

It uncovers universal critical exponents and amplitudes for thermodynamic curvatures in boundary CFTs, extending black hole thermodynamics insights to the dual field theories.

Findings

Critical exponents for boundary CFT curvatures are 2 and 1.

Universal amplitudes of curvature near criticality are independent of CFT dimensions.

Boundary CFT critical behavior mirrors that of bulk charged AdS black holes.

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 $AdS_{d}\times \mathbb{S}^{d+k}$ 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 $R_Nt^2$ is $\frac{1}{2}$ and $K_Nt$ is $-\frac{1}{2}$ when $t\rightarrow0^-$, whereas $R_Nt^2\approx \frac{1}{8}$ and $K_Nt\approx\frac{1}{4}$ in the limit $t\rightarrow0^+$ 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.