Supersymmetric Boundaries and Junctions in Four Dimensions

TL;DR

This paper thoroughly analyzes four-dimensional N=1 supersymmetric sigma-models with boundaries, establishing boundary terms, conditions, and junctions that preserve supersymmetry and generalize previous models.

Contribution

It introduces a comprehensive framework for boundary and junction conditions in supersymmetric sigma-models, including boundary potentials and couplings between different models.

Findings

Derived minimal boundary terms for off-shell supersymmetry

Characterized boundary conditions via Lagrangian submanifolds

Formulated supersymmetric junction conditions between different models

Abstract

We make a comprehensive study of (rigid) N=1 supersymmetric sigma-models with general K\"ahler potentials K and superpotentials w on four-dimensional space-times with boundaries. We determine the minimal (non-supersymmetric) boundary terms one must add to the standard bulk action to make it off-shell invariant under half the supersymmetries without imposing any boundary conditions. Susy boundary conditions do arise from the variational principle when studying the dynamics. Upon including an additional boundary action that depends on an arbitrary real boundary potential B one can generate very general susy boundary conditions. We show that for any set of susy boundary conditions that define a Lagrangian submanifold of the K\"ahler manifold, an appropriate boundary potential B can be found. Thus the non-linear sigma-model on a manifold with boundary is characterised by the tripel (K,B,w). We also discuss the susy coupling to new boundary superfields and generalize our results to supersymmetric junctions between completely different susy sigma-models, living on adjacent domains and interacting through a "permeable" wall. We obtain the supersymmetric matching conditions that allow us to couple models with different K\"ahler potentials and superpotentials on each side of the wall.