The Sound of Topology in the AdS/CFT Correspondence

TL;DR

This paper investigates how the topology and temperature of curved spaces influence two-point correlation functions in strongly coupled gauge theories via the AdS/CFT correspondence, revealing asymptotic behaviors and special temperature points.

Contribution

It provides new asymptotic expressions for correlation functions on curved spaces with various topologies, supported by numerical analysis, and identifies special temperatures affecting their structure.

Findings

Correlation functions depend on the relation between curvature and temperature.

A specific temperature exists for hyperbolic topology with analytical solutions.

Correlation poles exhibit non-smooth behavior near this temperature.

Abstract

Using the gauge/gravity correspondence, we study the properties of 2-point correlation functions of finite-temperature strongly coupled gauge field theories, defined on a curved space of general spatial topology with a dual black hole description. We derive approximate asymptotic expressions for the correlation functions and their poles, supported by exact numerical calculations, and study their dependence on the dimension of spacetime and the spatial topology. The asymptotic structure of the correlation functions depends on the relation between the spatial curvature and the temperature, and is noticeable when they are of the same order. In the case of a hyperbolic topology, a specific temperature is identified for which exact analytical solutions exist for all types of perturbations. The asymptotic structure of the correlation functions poles is found to behave in a non-smooth manner when approaching this temperature.