Heterotic Matrix theory with Wilson lines on the lightlike circle

TL;DR

This paper constructs a matrix model for the SO(32) Heterotic string with specific Wilson lines on a lightlike circle using T-duality, revealing a 1+1D O(N) theory with N influenced by momentum, winding, and quantum numbers.

Contribution

It introduces a matrix model for the heterotic string with Wilson lines on a lightlike circle, extending previous models via T-duality and analyzing the dependence of N on various quantum numbers.

Findings

Matrix model for SO(32) heterotic string with Wilson lines.

N depends on momentum, winding, and quantum numbers.

Discussion on extending the model to all Wilson lines.

Abstract

We develop a matrix model for the SO(32) Heterotic string with certain Wilson lines on the lightlike circle. This is done by using appropriate T-dualities. The method works for an infinite number of Wilson lines, but not for all. The matrix model is the theory on the D-string of type I wrapped on a circle with a SO(32) Wilson line on the circle. The radius of the circle depends on the Wilson line. This is a 1+1 dimensional O(N) theory on a circle. N depends not only on the momentum around the lightlike circle but also on the winding and SO(32) quantum numbers of the state. Perspectives for obtaining a matrix model for all Wilson lines are discussed.