Integrability + Supersymmetry + Boundary: Life on the Edge Is Not So Dull After All!

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.

Integrability of the boundary sine-Gordon model

“…In [3] and [4] he constructed boundary Lagrangians for the N = 1 and N = 2 cases, establishing supersymmetry and integrability which beforehand were considered to be incompatible in the presence of boundaries. For a nice review of this development see [5] and [8,9] for further related results. The authors of [9] especially provide an explanation for the appearance of fermionic boundary degrees of freedom following [10,11] by using a perturbative CFT approach.…”