The One Loop Effective Super-Potential and Non-Holomorphicity

TL;DR

This paper computes one-loop corrections to the superpotential and Kahler potential in various supersymmetric models, revealing the role of non-holomorphic contributions in N=2 Yang-Mills theory.

Contribution

It provides explicit calculations of one-loop Kahlerian and non-Kahlerian terms in multiple supersymmetric theories, including N=2 Yang-Mills, highlighting the non-holomorphic nature of certain corrections.

Findings

Calculated one-loop Kahlerian contributions in supersymmetric models.

Identified non-holomorphic contributions in N=2 Yang-Mills theory.

Demonstrated the origin of Kahlerian terms from non-holomorphic effects.

Abstract

We calculate the Kahlerian and the lowest order non-Kahlerian contributions to the one loop effective superpotential using super-Feynman graphs in the massless Wess-Zumino Model, the massive Wess-Zumino Model and N=1, U(1) gauge theory. We also calculate the Kahlerian term in Yang-Mills Theory for a general gauge group. Using this latter result we find the one loop Kahlerian contribution for N=2 Yang-Mills Theory in terms of N=1 superfields and we show that it can only come from non-holomorphic contributions to the N=2 effective potential.