Cohomological Field Theory Approach to Matrix Strings

TL;DR

This paper uses a cohomological field theory approach to exactly compute partition functions of IIA and IIB matrix string theories, confirming conjectures and suggesting model equivalences.

Contribution

It introduces a cohomological method to exactly evaluate partition functions of matrix string theories, providing proofs and evidence for model equivalences.

Findings

Exact partition function for IIA matrix string theory matches infra-red limit results.

Exact partition function for IIB matrix string theory matches IKKT model results.

Supports potential equivalence between different IIB matrix models.

Abstract

In this paper we consider IIA and IIB matrix string theories which are defined by two-dimensional and three-dimensional super Yang-Mills theory with the maximal supersymmetry, respectively. We exactly compute the partition function of both of the theories by mapping to a cohomological field theory. Our result for the IIA matrix string theory coincides with the result obtained in the infra-red limit by Kostov and Vanhove, and thus gives a proof of the exact quasi classics conjectured by them. Further, our result for the IIB matrix string theory coincides with the exact result of IKKT model by Moore, Nekrasov and Shatashvili. It may be an evidence of the equivalence between the two distinct IIB matrix models arising from different roots.