Symmetries of Heterotic String Theory

TL;DR

This paper investigates the symmetries of two-dimensional Heterotic string theory, identifying finite and infinite dimensional symmetry groups, conserved currents, and transformations, drawing parallels with Einstein-Maxwell equations.

Contribution

It introduces the affine $8, 24)$ symmetry algebra and constructs conserved currents, extending symmetry analysis methods to heterotic string theory.

Findings

Identification of finite dimensional groups $G'$ and $H'$

Construction of infinite conserved currents and affine symmetry algebra

Parallel between heterotic string symmetries and Einstein-Maxwell equations

Abstract

We study the symmetries of the two dimensional Heterotic string theory by following the approach of Kinnersley et al for the study of stationary-axially symmetric Einstein-Maxwell equations. We identify the finite dimensional groups $G'$ and $H'$ for the Einstein-Maxwell equations. We also give the constructions for the infinite number of conserved currents and the affine $\hat{o}(8, 24)$ symmetry algebra in this formulation. The generalized Ehlers and Harrison transformations are identified and a parallel between the infinite dimensional symmetry algebra for the heterotic string case with $\hat{sl}(3, R)$ that arise in the case of Einstein-Maxwell equations is pointed out.