A note on supersymmetric Yang-Mills thermodynamics

TL;DR

This paper investigates the thermodynamics of supersymmetric Yang-Mills theories across various dimensions by computing two-loop corrections and exploring non-analytic contributions, with implications for string theory and the Hagedorn transition.

Contribution

It provides the first detailed two-loop correction calculations for supersymmetric Yang-Mills thermodynamics in multiple dimensions and analyzes the non-analytic effects related to the 't Hooft coupling.

Findings

Computed two-loop free energy corrections for theories with 16, 8, and 4 supercharges.

Evaluated the first non-analytic 't Hooft coupling contribution in four dimensions.

Discussed implications for Hagedorn transition in string theory and Matrix strings.

Abstract

The thermodynamics of supersymmetric Yang-Mills theories is studied by computing the two-loop correction to the canonical free energy and to the equation of state for theories with 16, 8 and 4 supercharges in any dimension $4\leq d\leq 10$, and in two dimensions at finite volume. In the four-dimensional case we also evaluate the first non-analytic contribution in the 't Hooft coupling to the free energy, arising from the resummation of ring diagrams. To conclude, we discuss some applications to the study of the Hagedorn transition in string theory in the context of Matrix strings and speculate on the possible physical meaning of the transition.