Noncommutativity Parameter As a Field on the String Worldsheet

TL;DR

This paper models the noncommutativity parameter as a dynamic field on the string worldsheet, introducing its fermionic partner and deriving a corresponding two-dimensional action with symmetry analysis.

Contribution

It introduces a novel approach by treating the noncommutativity parameter as a bosonic field with a fermionic super-partner, enabling new star product formulations in superstring theory.

Findings

Derived a two-dimensional action for the noncommutativity parameter and its fermionic partner.

Established star products between various superstring worldsheet fields.

Analyzed the symmetries of the new action.

Abstract

We consider the noncommutativity parameter of the space-time as a bosonic worldsheet field. By finding a fermionic super-partner for it, we can find star products between the boson-boson, boson-fermion and fermion-fermion fields of superstring worldsheet and also between superfields of the worldsheet superspace. We find a two dimensional action for the noncommutativity parameter and its fermionic partner. We discuss the symmetries of this action.