Real-time observables from Euclidean thermal correlation functions

TL;DR

This paper demonstrates a method to extract real-time observables directly from Euclidean thermal correlation functions using the functional renormalisation group, avoiding traditional reconstruction methods, and applies it to determine shear viscosity.

Contribution

It introduces a novel approach to obtain real-time observables from Euclidean data, specifically in the quark-meson model, highlighting in-medium effects and spectral features.

Findings

In-medium effects can be extracted from Euclidean propagators' spatial momentum dependence.

Analytic features of the pion correlation function are characterized.

Non-perturbative shear viscosity is calculated from spectral contributions.

Abstract

In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional renormalisation group in the quark-meson model, we demonstrate that in-medium effects can be directly extracted from the spatial momentum dependence of the Euclidean propagators, in contrast to conventional approaches, which rely on the reconstruction from different Matsubara frequencies. As an application, we determine the analytic features that arise from the discrete spectral contribution to the pion correlation function, and calculate the non-perturbative shear viscosity arising from these states.