Boundary Effects in Super-Yang-Mills Theory

TL;DR

This paper investigates how boundaries affect supersymmetry in a three-dimensional $ ext{N}=2$ super-Yang-Mills theory, demonstrating that half of the supersymmetry can be preserved by adding a boundary Lagrangian.

Contribution

It introduces a method to preserve half of the supersymmetry in super-Yang-Mills theory with boundaries by constructing an appropriate boundary Lagrangian.

Findings

Half supersymmetry preserved with boundary Lagrangian

Derived Slavnov-Taylor identity for the boundary theory

Boundary effects explicitly analyzed in supersymmetric context

Abstract

In this paper, we shall analyse a three dimensional supersymmetry theory with $\mathcal{N} = 2$. The effective Lagrangian will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. In presence of a boundary the supersymmetry of this Lagrangian will be broken. However, it will be possible to preserve half the supersymmetry even in presence of a boundary. This will be done by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will obtain the Slavnov-Taylor Identity for this theory.