On quantum properties of the four-dimensional generic chiral superfield model

TL;DR

This paper develops a covariant method to evaluate one-loop quantum corrections in 4D supersymmetric K"ahler sigma models, revealing divergence structures and finite contributions analogous to super Yang-Mills theory.

Contribution

It introduces reparametrization covariant derivatives and techniques to compute the effective action, establishing an analogy with super Yang-Mills theory for the first time.

Findings

Divergences are characterized by supersymmetric WZNW terms.

Leading finite contributions are explicitly calculated.

Methodology unifies quantum correction evaluation in supersymmetric sigma models.

Abstract

We study a problem of systematical evaluation of the quantum corrections for general 4D supersymmetric K\"ahler sigma models with chiral and antichiral superpotentials. Using manifestly reparametrization covariant techniques (the background-quantum splitting and proper-time representation) in the ${\cal N}=1$ superspace we show how to define unambiguously the one-loop effective action. We introduce the reparametrization covariant derivatives acting on superfields and prove that their algebra is analogous to algebra in super Yang-Mills (SYM) theory. This analogy allows us to use for evaluation of the effective action in the theory under consideration methods developed for SYM theory. The divergencies for the model are obtained. It is shown that on general K\"ahler manifold the one-loop counterterms have the structure of a supersymmetric WZNW term. Leading finite contribution in covariant derivative expansion of the one-loop effective action (superfield $a_3$ coefficient) is calculated.