Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group

TL;DR

This paper introduces a straightforward FRG-based method for calculating real-time correlation functions in the O(N) model, providing insights into mesonic spectral functions and the dynamical nature of the sigma meson.

Contribution

It presents a novel truncation scheme within the FRG framework for real-time n-point functions, enabling analytic continuation and spectral analysis in the scalar O(N) model.

Findings

Computed mesonic spectral functions using the new method

Analyzed the scale dependence of 2-point functions

Provided insights into the dynamical origin of the sigma meson

Abstract

In the framework of the functional renormalization group (FRG) we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.