Branched Coverings and Interacting Matrix Strings in Two Dimensions

TL;DR

This paper develops a lattice gauge theory for a group combining permutation and U(1) symmetries, modeling branched string coverings with gauge fields on two-dimensional surfaces, extending Matrix String theory.

Contribution

It introduces a comprehensive lattice gauge theory for G_N, capturing arbitrary string branching and interactions in a non-supersymmetric two-dimensional setting.

Findings

Formulation of the G_N lattice gauge theory including arbitrary branch points

Classification of irreducible representations of G_N

Description of string splitting and joining processes

Abstract

We construct the lattice gauge theory of the group G_N, the semidirect product of the permutation group S_N with U(1)^N, on an arbitrary Riemann surface. This theory describes the branched coverings of a two-dimensional target surface by strings carrying a U(1) gauge field on the world sheet. These are the non-supersymmetric Matrix Strings that arise in the unitary gauge quantization of a generalized two-dimensional Yang-Mills theory. By classifying the irreducible representations of G_N, we give the most general formulation of the lattice gauge theory of G_N, which includes arbitrary branching points on the world sheet and describes the splitting and joining of strings.