N=1 supersymmetric sigma model with boundaries, I

TL;DR

This paper investigates boundary conditions in an N=1 supersymmetric sigma model, revealing compatibility with superconformal symmetry and identifying geometric structures like almost product structures in the target space.

Contribution

It provides a comprehensive analysis of boundary conditions compatible with N=1 superconformal symmetry and interprets them geometrically in the target space.

Findings

Boundary conditions preserving superconformal symmetry identified.

Partial integrability and almost product structures in target space established.

Two methods of analysis yield consistent results.

Abstract

We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.