Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory

TL;DR

This paper investigates how boundary effects influence the gauge and supersymmetric invariance of the BLG theory, proposing boundary terms and degrees of freedom to restore these symmetries, leading to a generalized boundary model.

Contribution

It introduces a boundary theory for the BLG model that restores gauge and supersymmetry invariance by adding boundary degrees of freedom and boundary terms.

Findings

Boundary terms restore supersymmetry and gauge invariance.

Boundary theory generalizes gauged Wess-Zumino-Witten model.

Boundary degrees of freedom cancel boundary variations.

Abstract

In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by the generators of the Lie 3-algebra. The gauge and supersymmetry variations of the boundary theory will exactly cancel the boundary terms generated by the gauge and supersymmetric variations of the bulk theory.