The Super-Liouville-Equation on the Half-Line

TL;DR

This paper derives a recursive formula for integrals of motion in super-Liouville theory, explores boundary interactions, and compares supersymmetric and free-parameter cases in super-Toda theory based on affine superalgebra.

Contribution

It introduces a recursive formula for integrals of motion and analyzes boundary interactions in super-Liouville and super-Toda theories, highlighting supersymmetry constraints.

Findings

Recursive formula for integrals of motion derived.

Boundary interactions in super-Liouville theory determined by supersymmetry.

Super-Toda theory boundary interactions have free parameters.

Abstract

A recursive formula for an infinity of integrals of motion for the super-Liouville theory is derived. The integrable boundary interactions for this theory and the super-Toda theory based on the affine superalgebra $B^{(1)} (0,1)$ are computed. In the first case the boundary interactions are unambiguously determined by supersymmetry, whilst in the latter case there are free parameters.