Supersymmetric Toda Field Theories

TL;DR

This paper develops new supersymmetric versions of Conformal Toda and Affine Toda field theories, expanding their symmetry structures and providing explicit constructions for these extensions.

Contribution

It introduces novel supersymmetric extensions of Toda field theories, specifically (1,1) and (1,0) supersymmetries, using methods adapted from sigma model extensions.

Findings

Conformal Toda admits a (1,1)-supersymmetric extension.

A^{(1)}_N Affine Toda admits a (1,0)-supersymmetric extension.

Theories are constructed using methods similar to those for sigma models.

Abstract

We present new supersymmetric extensions of Conformal Toda and $A^{(1)}_N$ Affine Toda field theories. These new theories are constructed using methods similar to those that have been developed to find supersymmetric extensions of two-dimensional bosonic sigma models with a scalar potential. In particular, we show that the Conformal Toda field theory admits a (1,1)-supersymmetric extension, and the $A^{(1)}_N$ Affine Toda field admits a (1,0)-supersymmetric extension.