On the Perturbative Evaluation of Thermal Green's Functions in the Bulk and Shear Channels of Yang-Mills Theory

TL;DR

This thesis reviews recent perturbative methods for calculating energy momentum tensor correlators in high-temperature Yang-Mills theory, focusing on spectral functions, operator product expansions, and comparison with lattice and gravity results.

Contribution

It develops new perturbative techniques for evaluating thermal Green's functions in bulk and shear channels of Yang-Mills theory, enhancing understanding of transport coefficients.

Findings

Agreement with lattice and gravity calculations

Extraction of transport coefficients from Euclidean data

Advancement of perturbative methods for spectral functions

Abstract

In this PhD thesis, I will review recent progress in perturbative studies of energy momentum tensor correlators in high-temperature Yang-Mills theory. After briefly introducing the necessary tools and physical motivation, I proceed to discuss the machinery developed for the extraction of next-to-leading order Operator Product Expansions and thermal spectral functions and to introduce the results obtained in the bulk and shear channels of Yang-Mills theory. Particular emphasis is placed on the comparison of the results with recent lattice and gauge/gravity calculations, as well as on discussing their use in extracting the corresponding transport coefficients from Euclidean lattice data.