Summing up Non-anti-commutative Kaehler potential

TL;DR

This paper derives a non-perturbative formula for the component action of N=1/2 supersymmetric chiral models with non-anti-commutative deformation, extending the understanding of scalar potentials in such theories.

Contribution

It provides a simple, non-perturbative formula for the component action of NAC-deformed supersymmetric models with arbitrary Kaehler and superpotentials.

Findings

Derived a non-perturbative component action formula for NAC-deformed models.

Eliminated auxiliary fields for single chiral superfield case.

Calculated NAC deformation of the CP(1) sigma-model with arbitrary superpotential.

Abstract

We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the Non-Anti-Commutative (NAC) deformation of a generic four-dimensional N=1 supersymmetric non-linear sigma-model described by arbitrary Kaehler superpotential and scalar superpotential. The auxiliary integrations responsible for fuzziness are eliminated in the case of a single chiral superfield. The scalar potential in components is derived by eliminating the auxiliary fields. The NAC-deformation of the CP(1) Kaehler non-linear sigma-model with an arbitrary scalar superpotential is calculated as an example.