Integrability + Supersymmetry + Boundary: Life on the edge is not so dull after all!

TL;DR

This paper reviews integrability and supersymmetry in boundary models, specifically constructing actions for boundary sine-Gordon models with fermionic boundary degrees of freedom, highlighting the rich structure at boundaries.

Contribution

It introduces fermionic boundary degrees of freedom in boundary sine-Gordon models, advancing the understanding of integrable supersymmetric boundary theories.

Findings

Construction of N=1 and N=2 boundary sine-Gordon actions

Inclusion of fermionic boundary degrees of freedom

Enhanced understanding of boundary integrability and supersymmetry

Abstract

After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N=1 and N=2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary degrees of freedom in the boundary actions.