Noncommutative associative superproduct for general supersymplectic forms

TL;DR

This paper introduces a new associative superproduct for supersymplectic forms, enabling explicit treatment of non(anti)commutative field theories in string backgrounds while preserving super Poincare symmetry.

Contribution

It generalizes deformation quantization to superspace considering noncommutativity in the tangent bundle, maintaining supersymmetry and chirality.

Findings

Defines a noncommutative superproduct for supersymplectic forms.

Generalizes Fedosov's deformation quantization to superspace.

Recovers the Moyal product in a specific case.

Abstract

We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantization a la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincare symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories.