Superconformal Affine Liouville Theory

TL;DR

This paper introduces a new superconformal and integrable model based on a twisted affine superalgebra, extending the conformal affine Liouville theory to include supersymmetry and analyzing its classical solutions and algebraic structures.

Contribution

It constructs a superconformal integrable model from a twisted affine superalgebra, connecting it to super-Liouville and super sinh-Gordon theories, and derives classical solutions and algebraic frameworks.

Findings

Model reduces to super-Liouville and super sinh-Gordon theories under limits

Provides reconstruction formulae for classical solutions

Derives classical r-matrices and exchange algebras

Abstract

We present a superconformally invariant and integrable model based on the twisted affine Kac-Moody superalgebra $\hat{osp(2|2)}^{(2)}$ which is the supersymmetrization of the purely bosonic conformal affine Liouville theory recently proposed by Babelon and Bonora. Our model reduces to the super-Liouville or to the super sinh-Gordon theories under certain limit conditions and can be obtained, via hamiltonian reduction, from a superspace WZNW model with values in the corresponding affine KM supergroup. The reconstruction formulae for classical solutions are given. The classical $r$-matrices in the homogeneous grading and the exchange algebras are worked out.