Non-anticommutativity in Presence of a Boundary

TL;DR

This paper explores non-anticommutative supersymmetric field theories on three-dimensional manifolds with boundaries, demonstrating how to preserve partial supersymmetry and analyze supersymmetry breaking effects due to non-anticommutativity.

Contribution

It constructs a three-dimensional $ ext{N}=1/2$ supersymmetric theory incorporating boundary effects and non-anticommutativity, extending previous understanding beyond four-dimensional cases.

Findings

Partial supersymmetry is preserved with boundary modifications.

Non-anticommutativity causes partial supersymmetry breaking.

A novel $ ext{N}=1/2$ supersymmetric theory in 3D is developed.

Abstract

In this paper we consider non-anticommutative field theories in $\mathcal{N} =2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry even in the presence of a boundary. We also analyse the partial breaking of supersymmetry caused by non-anticommutativity between fermionic coordinates. Unlike in four dimensions, in three dimensions a theory with $\mathcal{N} =1/2$ supersymmetry cannot be obtained by a non-anticommutative deformation of an $\mathcal{N} =1$ theory. However, in this paper we construct a three dimensional theory with $\mathcal{N} =1/2$ supersymmetry by studying a combination of non-anticommutativity and boundary effects, starting from $\mathcal{N} =2$ supersymmetry.