Minkowski-space correlators in AdS/CFT correspondence: recipe and applications

TL;DR

The authors develop a practical Minkowski-space AdS/CFT prescription to extract retarded two-point correlators directly from gravity, addressing limitations of Euclidean analytic continuation for real-time thermal physics. They validate the method by reproducing zero-temperature AdS/CFT results, computing finite-temperature BTZ/CFT correlators, and showing that retarded poles align with BTZ quasinormal modes. Applying the prescription to thermal N=4 SYM yields a strong-coupling prediction for the Chern-Simons diffusion rate, illustrating the approach's utility for real-time transport at strong coupling. While the framework focuses on two-point functions, it provides a concrete, testable tool for holographic real-time dynamics and hydrodynamic analyses, with clear avenues for extension to higher-point functions.

Abstract

We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature N=4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.