Spectral reconstruction based on dimensional reduction in high-temperature gauge theories

TL;DR

This paper introduces a spectral reconstruction method for high-temperature gauge theories that integrates semi-classical real-time evolution into lattice QCD, improving spectral resolution at high temperatures.

Contribution

The authors develop a novel spectral reconstruction workflow that combines dimensional reduction and semi-classical evolution, enhancing spectral analysis in high-temperature gauge theories.

Findings

Accurately reproduces quantum spectral functions in a (1+1)-D Abelian gauge theory.

Demonstrates improved spectral resolution over traditional Euclidean methods.

Shows feasibility of applying the method to lattice QCD at high temperatures.

Abstract

We propose a numerical spectral reconstruction workflow for high-temperature gauge theories that incorporates elements of semi-classical real-time evolution directly into standard lattice QCD simulations via high-temperature dimensional reduction, thus counteracting the deterioration of Euclidean-time correlators at high temperatures. With a moderate numerical cost, our method allows to estimate spectral functions with parametrically better frequency resolution as compared with spectral reconstruction methods based on Euclidean-time correlators alone. The method is tested on a simple (1+1)-dimensional Abelian gauge theory with fermions, where our method precisely reproduces the full quantum spectral functions calculated using exact numerical diagonalization in the high-temperature, weak-coupling regime. We also demonstrate the feasibility of our approach by applying it to light-quark meson correlators in lattice QCD deep in the deconfinement regime.