标题： AdS/CFT中的精确低温Green函数：从Heun到合流Heun 显示英文标题

标题： Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun

摘要： 我们在有限密度和低温下获得了CFT$_4$（与RN-AdS$_5$黑色薄片对偶）的带电标量算符相关函数的精确表达式。 我们利用了源自Liouville共形场论以及AGT对应关系的黑洞扰动理论中的Heun连接问题的最新进展。 该连接问题在一个瞬时子计数参数的微扰展开中被解决，此参数在固定$\omega/T$的双尺度极限下受控于$\omega, T \to 0$。 这提供了对Heun方程的合流极限下零温分支切割出现的解析控制。 从Green函数中，我们提取了关于全息超导体临界温度以及具有能隙和无能隙的低温准正规模式的色散关系的解析结果。 我们展示了与数值结果的精确一致。 显示英文摘要

摘要： We obtain exact expressions for correlation functions of charged scalar operators at finite density and low temperature in CFT$_4$ dual to the RN-AdS$_5$ black brane. We use recent developments in the Heun connection problem in black hole perturbation theory arising from Liouville CFT and the AGT correspondence. The connection problem is solved perturbatively in an instanton counting parameter, which is controlled in a double-scaling limit where $\omega, T \to 0$ holding $\omega/T$ fixed. This provides analytic control over the emergence of the zero temperature branch cut as a confluent limit of the Heun equation. From the Green's function we extract analytic results for the critical temperature of the holographic superconductor, as well as dispersion relations for both gapped and gapless low temperature quasinormal modes. We demonstrate precise agreement with numerics.