Matrix String Partition Functions

TL;DR

This paper computes the partition function of a reduced super-Yang--Mills theory on a torus, showing that a quasi-classical approach reproduces known results and supports the idea of an exact calculation in Matrix string theory.

Contribution

It provides a quasi-classical evaluation of the Ramond partition function that matches exact results, suggesting the potential exactness of this approximation in Matrix string theory.

Findings

Quasi-classical calculation reproduces the partition function exactly.

Results support the interpretation of strings wrapping the space-time torus.

Extrapolation to ultraviolet limit matches known SYM partition results.

Abstract

We evaluate quasi-classically the Ramond partition function of Euclidean D=10 U(N) super-Yang--Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasi-classical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasi-classical calculation might be exact.