Finite temperature spectral functions in the O(N)-model

TL;DR

This paper develops a numerical framework using the Functional Renormalization Group to compute spectral functions of the O(N)-model at finite temperature, preserving Lorentz invariance, and applies it to analyze pion and sigma mesons across phase transitions.

Contribution

It introduces a fully numerical, Lorentz-invariant FRG approach for finite temperature spectral functions in the O(N)-model, enabling detailed analysis of mesonic spectral properties.

Findings

Spectral functions for pions and sigma mesons across temperature range are computed.

The framework preserves Euclidean and Minkowski invariance, facilitating future applications.

Insights into the relationship between Euclidean and real-time two-point functions are discussed.

Abstract

We directly calculate spectral functions in the O(N)-model at finite temperature within the framework of the Functional Renormalization group. Special emphasis is put on a fully numerical framework involving four-dimensional regulators preserving Euclidean O(4) and Minkowski Lorentz invariance, an important prerequisite for future applications. Pion and sigma meson spectral functions are calculated for a wide range of temperatures across the phase transition illustrating the applicability of the general framework for finite temperature applications. In addition, various aspects concerning the interplay between the Euclidean and real time two-point function are discussed.