Statistical mechanics for dilatations in N=4 super Yang--Mills theory

TL;DR

This paper develops a matrix model approach to analyze the thermal behavior of composite operators in N=4 super Yang--Mills theory, providing insights into their anomalous dimensions at finite temperature.

Contribution

It introduces a thermal effective action for a matrix model of composite operators, computed at one-loop level in both high and low temperature regimes.

Findings

Thermal effective action derived for the matrix model.

Results obtained in high and low temperature limits.

Insights into anomalous dimensions at finite temperature.

Abstract

Matrix model describing the anomalous dimensions of composite operators in $\mathcal{N}=4$ super Yang--Mills theory up to one-loop level is considered at finite temperature. We compute the thermal effective action for this model, which we define as the log of the partition function restricted to the states of given fixed length and spin. The result is obtained in the limits of high and low temperature.