Boundary Effects in Super-Yang-Mills Theory

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.