A Note on Supersymmetry in Noncommutative Field Theories

TL;DR

This paper demonstrates that a specific supergravity solution representing D3-branes with a 2-form background preserves 16 supersymmetries and is dual to a noncommutative Yang-Mills theory, highlighting supersymmetry properties in noncommutative field theories.

Contribution

It explicitly constructs the unbroken supersymmetry transformation parameter for a supergravity solution with noncommutative features, revealing supersymmetry preservation in this context.

Findings

The supergravity solution has 16 supersymmetries.

The solution is dual to a noncommutative Yang-Mills theory.

Supersymmetry is explicitly demonstrated in the presence of a 2-form background.

Abstract

We show that a solution of the type IIB supergravity representing D3-branes in the presence of a 2-form background has 16 supersymmetries by explicitly constructing the transformation parameter of unbroken supersymmetry. This solution is dual to a noncommutative Yang-Mills theory in a certain limit.