Generic chiral superfield model on nonanticommutative N=1/2 superspace

TL;DR

This paper develops a comprehensive framework for a generic nonanticommutative chiral-antichiral superfield model in four-dimensional superspace, deriving explicit component Lagrangians and exploring auxiliary field elimination and potential corrections.

Contribution

It introduces a general nonanticommutative supersymmetric model with arbitrary potentials, providing explicit component expressions and a resummation of the classical action.

Findings

Derived explicit component Lagrangian including auxiliary fields.

Resummed the infinite series into a compact deformed Lagrangian.

Calculated the first perturbative correction to the scalar potential.

Abstract

We consider the generic nonanticommutative model of chiral-antichiral superfields on ${\cal N}={1\over 2}$ superspace. The model is formulated in terms of an arbitrary K\"ahlerian potential, chiral and antichiral superpotentials and can include the nonanticommutative supersymmetric sigma-model as a partial case. We study a component structure of the model and derive the component Lagrangian in an explicit form with all auxiliary fields contributions. We show that the infinite series in the classical action for generic nonanticommutative model of chiral-antichiral superfields in D=4 dimensions can be resumed in a compact expression which can be written as a deformation of standard Zumino's lagrangian and chiral superpotential. Problem of eliminating the auxiliary fields in the generic model is discussed and the first perturbative correction to the effective scalar potential is obtained.