规范/引力对偶中边界共形场论热力学几何的泛临界性
Universal criticality of thermodynamic geometry for boundary conformal field theories in gauge/gravity duality
摘要：
根据最近的AdS/CFT解释\cite{Karch:2015rpa}，其中改变宇宙学常数$Λ$对应于改变场论所在空间的曲率半径，我们研究了与$d$维带电反德西特（AdS）黑洞对偶的热边界共形场论（CFT）的热力学曲率的临界性，嵌入在$D$维M理论/超弦启发模型中，具有带有$D=2d+k$的$AdS_{d}\times \mathbb{S}^{d+k}$时空。与块体\cite{HosseiniMansoori:2020jrx}中带电AdS黑洞的临界特征类似，边界CFT的归一化内禀曲率$R_N$和外禀曲率$K_N$分别具有临界指数2和1。在这方面，当$t\rightarrow0^-$，而$R_Nt^2\approx \frac{1}{8}$和$K_Nt\approx\frac{1}{4}$在极限$t\rightarrow0^+$，其中$t=T/T_c-1$是具有临界温度$T_{c}$的温度参数时，$R_Nt^2$的通用幅度是$\frac{1}{2}$，$K_Nt$是$-\frac{1}{2}$。有趣的是，这些临界振幅是独立的热CFT维度的数量和显着相似的高维带电的AdS黑洞的散装。
英文摘要：
According to more recent AdS/CFT interpretation \cite{Karch:2015rpa}, in which varying cosmological constant $Λ$ 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.
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