Field Theory in Noncommutative Minkowski Superspace

TL;DR

This paper develops a consistent framework for non(anti)commutative Minkowski superspace, extending previous Euclidean models, and presents a Hermitian, Lorentz-invariant Wess-Zumino Lagrangian with additional terms due to non(anti)commutativity.

Contribution

It introduces a novel algebra and star-product for non(anti)commutative Minkowski superspace, enabling the construction of a Hermitian, Lorentz-invariant supersymmetric Lagrangian.

Findings

The algebra for supercoordinates is consistent and well-defined.

A star-product is constructed for the non(anti)commutative superspace.

The Wess-Zumino Lagrangian includes two extra terms from non(anti)commutativity, maintaining Hermiticity and Lorentz invariance.

Abstract

There is much discussion of scenarios where the space-time coordinates x^\mu are noncommutative. The discussion has been extended to include nontrivial anticommutation relations among spinor coordinates in superspace. A number of authors have studied field theoretical consequences of the deformation of N=1 superspace arising from nonanticommutativity of coordinates \theta, while leaving \bar{theta}'s anticommuting. This is possible in Euclidean superspace only. In this note we present a way to extend the discussion by making both \theta and \bar{theta} coordinates non-anticommuting in Minkowski superspace. We present a consistent algebra for the supercoordinates, find a star-product, and give the Wess-Zumino Lagrangian L_{WZ} within our model. It has two extra terms due to non(anti)commutativity. The Lagrangian in Minkowski superspace is always manifestly Hermitian and for L_{WZ} it preserves Lorentz invariance.