Chiral effective potential in ${\cal N}={1/2}$ non-commutative Wess-Zumino model

TL;DR

This paper derives an exact one-loop chiral effective potential for the ${ m abla}={1/2}$ noncommutative Wess-Zumino model using heat kernel techniques, providing a systematic way to compute its series expansion.

Contribution

It presents the exact integral form of the one-loop effective potential and a systematic method to calculate its series coefficients, including a closed-form sum of derivative-free terms.

Findings

Exact integral representation of the one-loop effective potential.

Systematic procedure for calculating series coefficients.

Closed-form sum of terms without derivatives.

Abstract

We study a structure of holomorphic quantum contributions to the effective action for ${\cal N}={1/2}$ noncommutative Wess-Zumino model. Using the symbol operator techniques we present the one-loop chiral effective potential in a form of integral over proper time of the appropriate heat kernel. We prove that this kernel can be exactly found. As a result we obtain the exact integral representation of the one-loop effective potential. Also we study the expansion of the effective potential in a series in powers of the chiral superfield $\Phi$ and derivative $D^2{\Phi}$ and construct a procedure for systematic calculation of the coefficients in the series. We show that all terms in the series without derivatives can be summed up in an explicit form.