Supersymmetric Boundary Conditions for the N=2 Sigma Model

TL;DR

This paper clarifies supersymmetric boundary conditions for the N=2 sigma model, confirming known results about supersymmetric cycles while identifying a new constraint on boundary actions that challenges previous assumptions.

Contribution

It provides a detailed analysis of boundary conditions in the N=2 sigma model and introduces a new constraint on boundary actions not previously recognized.

Findings

Confirmed existing results on supersymmetric cycles

Identified a new constraint on boundary actions

Highlighted discrepancies with previously used boundary actions

Abstract

We clarify the discussion of N=2 supersymmetric boundary conditions for the classical d=2, N=(2,2) Non-Linear Sigma Model on an infinite strip. Our conclusions about the supersymmetric cycles match the results found in the literature. However, we find a constraint on the boundary action that is not satisfied by many boundary actions used in the literature.