Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory

TL;DR

This paper introduces a deformation of four-dimensional N=1 superspace where odd coordinates satisfy a Clifford algebra, leading to new noncommutative field theories with string theory origins and preserved antichiral structures.

Contribution

It develops a consistent deformation of superspace with Clifford algebra relations, analyzes the resulting field theories, and connects them to string theory in a graviphoton background.

Findings

Deformation leads to noncommutative superspace with modified coordinate relations.

Gauge interactions can be expressed in standard form despite deformation.

Deformed theories retain an antichiral ring with usual properties.

Abstract

We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular, the ordinary spacetime coordinates $x$ cannot commute. We study chiral superfields and vector superfields and their interactions. As in ordinary noncommutative field theory, a change of variables allows us to express the gauge interactions in terms of component fields which are subject to standard gauge transformation laws. Unlike ordinary noncommutative field theories, the change of the Lagrangian is a polynomial in the deformation parameter. Despite the deformation, the noncommutative theories still have an antichiral ring with all its usual properties. We show how these theories with precisely this deformation arise in string theory in a graviphoton background.