New matrix formalism for heterotic string theory on a torus

TL;DR

This paper introduces a novel matrix-based Lagrangian formalism for low-energy heterotic string theory compactified on a torus, simplifying the description of symmetries and potentials.

Contribution

It develops a unified matrix formalism using a single scalar potential to describe heterotic string theory with multiple U(1) gauge fields on a torus.

Findings

Unified matrix potential formalism for heterotic string theory.

Explicit linear transformation properties under charging symmetries.

Simplification of the low-energy effective theory description.

Abstract

A new Lagrange formalism based on the use of a single scalar (d+1)X(d+1+n) matrix potential is developed for the low-energy heterotic string theory with n U(1) gauge fields compactified from d+3 to 3 dimensions on a torus. This formalism also includes three pairs on-shell defined scalar and vector matrix potentials of the dimensions (d+1)X(d+1), (d+1)X(d+1+n) and (d+1+n)X(d+1+n). All these potentials undergo linear transformations when the group of charging symmetries acts.