Heterotic Matrix String Theory and Riemann Surfaces

TL;DR

This paper extends Matrix String Theory to the heterotic case, deriving instanton solutions related to Riemann surfaces, and shows that in the strong coupling limit, the theory reproduces heterotic string dynamics with expected interaction scaling.

Contribution

It introduces the Heterotic Matrix String Theory, formulates instanton equations, and demonstrates their solutions correspond to branched coverings of Riemann surfaces, connecting gauge theory to heterotic string interactions.

Findings

Instanton solutions characterized by branched Riemann surfaces.

Strong coupling limit reproduces heterotic string action.

Amplitude scales with string coupling as expected for heterotic strings.

Abstract

We extend the results found for Matrix String Theory to Heterotic Matrix String Theory, i.e. to a 2d O(N) SYM theory with chiral (anomaly free) matter and N=(8,0) supersymmetry. We write down the instanton equations for this theory and solve them explicitly. The solutions are characterized by branched coverings of the basis cylinder, i.e. by compact Riemann surfaces with punctures. We show that in the strong coupling limit the action becomes the heterotic string action plus a free Maxwell action. Moreover the amplitude based on a Riemann surface with p punctures and h handles is proportional to g^{2-2h-p}, as expected for the heterotic string interaction theory with string coupling g_s=1/g.