N=1 supersymmetric sigma model with boundaries, II

TL;DR

This paper analyzes boundary conditions in N=1 supersymmetric sigma models with boundaries and B-fields, revealing their geometric interpretation and proposing a new structure related to target space geometry.

Contribution

It provides a comprehensive description of boundary conditions compatible with N=1 superconformal symmetry and introduces a novel geometric perspective involving deformations of almost product structures.

Findings

Boundary conditions correspond to maximal integral submanifolds.

A new geometric structure, the deformation of an almost product structure, is proposed.

The analysis aids in formulating consistent actions for supersymmetric sigma models.

Abstract

We consider the N=1 supersymmetric two-dimensional non-linear sigma model with boundaries and nonzero B-field. By analysing the appropriate currents we describe the full set of boundary conditions compatible with N=1 superconformal symmetry. Using this result the problem of finding a correct action is discussed. We interpret the supersymmetric boundary conditions as a maximal integral submanifold of the target space manifold, and speculate about a new geometrical structure, the deformation of an almost product structure.