Inheritance principle and Non-renormalization theorems at finite temperature

TL;DR

This paper proves an inheritance principle in weakly coupled SU(N) gauge theories on compact manifolds, showing that certain correlation functions at finite temperature relate to zero-temperature ones, preserving some non-renormalization theorems despite broken symmetries.

Contribution

It provides a general proof of the inheritance principle and demonstrates the survival of non-renormalization theorems at finite temperature in gauge theories.

Findings

Finite temperature correlation functions relate to zero-temperature functions via image sums.

Non-renormalization theorems of $ n=4$ SYM persist at finite temperature.

The inheritance principle applies to a class of compact manifolds like $S^3$.

Abstract

We present a general proof of an ``inheritance principle'' satisfied by a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$). In the large $N$ limit, finite temperature correlation functions of gauge invariant single-trace operators in the low temperature phase are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. As a consequence, various non-renormalization theorems of $\NN=4$ Super-Yang-Mills theory on $S^3$ survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.