Non-anticommutative Supersymmetric Field Theory and Quantum Shift

TL;DR

This paper develops a method to map commutative supersymmetric field theories to non-anticommutative versions using twist deformations, preserving some symmetries while quantifying their violation.

Contribution

It introduces a decomposition of Grassmann coordinates into geometrical and quantum shift operators, enabling a systematic mapping to non-anticommutative supersymmetric models.

Findings

Derived the non-anticommutative Wess-Zumino Lagrangian

Analyzed super-Poincaré symmetry preservation and violation

Provided a framework for twist deformation in superspace

Abstract

Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess-Zumino model in commutative field theory and derive the corresponding non-anticommutative Lagrangian. Based on the theory of twist deformations of Hopf algebras, we comment the preservation of the (initial) N=1 super-Poincar\'e {\it algebra} and on the consequent super-Poincar\'e invariant interpretation of the discussed model, but also provide a measure for the violation of the super-Poincar\'e symmetry.