Analytic structure of stress-energy response functions and new Kubo formulae

TL;DR

This paper analyzes the analytic structure of stress-energy correlation functions in relativistic hydrodynamics, deriving new Kubo formulae for transport coefficients in the low-frequency, low-wavenumber regime.

Contribution

It determines the analytic structure of stress-energy correlations and introduces new Kubo formulae, clarifying the limits involved in transport coefficient calculations.

Findings

Derived the low-frequency, low-wavenumber analytic structure of stress-energy correlation functions.

Introduced new Kubo formulae for transport coefficients in relativistic hydrodynamics.

Clarified the impact of higher-order terms on the interpretation of relaxation times.

Abstract

Determining the transport properties of Quark-Gluon Plasma is one of the most important aspects of relativistic heavy ion collision studies. Field-theoretical calculations of the transport coefficients such as the shear and bulk viscosities require Kubo formulae which in turn require real-time correlation functions of stress-energy tensors. Consequently, knowing the analytic structure of these correlation functions is essential in any such studies. Using the energy-conservation laws and the results from the gravity-hydrodynamics analysis, we determine the low-frequency and low-wavenumber analytic structures of all stress-energy correlation functions in the rest frame of the medium. By comparing with the diffusion and sound spectra from the second-order and the third-order relativistic hydrodynamics, various new Kubo formulae are derived in the limit where the zero-frequency limit is taken first. We also show that the meaning of the Kubo formulae for relaxation times can change when higher-order terms are added to hydrodynamics. A subtle issue of taking the zero frequency and zero wavenumber limits when using skeleton diagrams is addressed as well.