A Field Theoretical Model in Noncommutative Minkowski Superspace

TL;DR

This paper develops a consistent field theoretical model in Minkowski N=1 superspace with deformed supercoordinate algebra inspired by super-string theory, introducing non(anti)commutativity while preserving key superspace properties.

Contribution

It extends non(anti)commutative superspace models to Minkowski space, providing a real star product and a Hermitian Lagrangian with Lorentz-invariant corrections.

Findings

Constructed a consistent supercoordinate algebra.

Developed a real star product preserving (anti)chirality.

Derived a Hermitian Wess-Zumino Lagrangian with Lorentz-invariant corrections.

Abstract

In this talk we present a field theoretical model constructed in Minkowski N=1 superspace with a deformed supercoordinate algebra. Our study is motivated in part by recent results from super-string theory, which show that in a particular scenario in Euclidean superspace the spinor coordinates \theta do not anticommute. Field theoretical consequences of this deformation were studied in a number of articles. We present a way to extend the discussion to Minkowski space, by assuming non-vanishing anticommutators for both \theta, and \bar{\theta}. We give a consistent supercoordinate algebra, and a star product that is real and preserves the (anti)chirality of a product of (anti)chiral superfields. We also give the Wess-Zumino Lagrangian that gains Lorentz-invariant corrections due to non(anti)commutativity within our model. The Lagrangian in Minkowski superspace is also always manifestly Hermitian.