New supersymmetric generalization of the Liouville equation

TL;DR

This paper introduces new supersymmetric extensions of the Liouville equation derived from a geometric approach to superstring dynamics, including zero curvature representations and Bäcklund transformations.

Contribution

It provides novel $n=(1,1)$ and $n=(1,0)$ supersymmetric generalizations of the Liouville equation based on a geometric framework for superstring classical dynamics.

Findings

Developed supersymmetric Liouville equations for specific superspaces

Established zero curvature representations for these equations

Constructed Bäcklund transformations for the supersymmetric equations

Abstract

We present new $n=(1,1)$ and $n=(1,0)$ supersymmetric generalization of the Liouville equation, which originate from a geometrical approach to describing the classical dynamics of Green--Schwarz superstrings in $N=2,~D=3$ and $N=1,~D=3$ target superspace. Considered are a zero curvature representation and B\"acklund transformations associated with the supersymmetric non--linear equations.