Non(anti)commutative superspace with coordinate-dependent deformation

TL;DR

This paper explores a coordinate-dependent non(anti)commutative superspace, demonstrating the preservation of a deformed supersymmetry and constructing a consistent deformed super Yang-Mills theory with matter, linking deformation parameters to graviphoton backgrounds.

Contribution

It introduces a novel coordinate-dependent deformation in superspace and constructs a consistent deformed super Yang-Mills theory with matter fields, extending previous constant-deformation frameworks.

Findings

Chiral ${ m N}=1/2$ supersymmetry can be defined with coordinate-dependent deformation.

Chiral and antichiral superfields remain closed under the deformed product.

A consistent deformed super Yang-Mills theory is possible under specific conditions on the deformation.

Abstract

We consider non(anti)commutative superspace with coordinate dependent deformation parameters $C^{\alpha\beta}$. We show that a chiral ${\cal N}=1/2$ supersymmetry can be defined and that chiral and antichiral superfields are still closed under the Moyal-Weyl associative product implementing the deformation. A consistent ${\cal N}=1/2$ Super Yang-Mills deformed theory can be constructed provided $C^{\alpha\beta}$ satisfies a suitable condition which can be connected with the graviphoton background at the origin of the deformation. After adding matter we also discuss the Konishi anomaly and the gluino condensation.