On metric geometry of conformal moduli spaces of four-dimensional superconformal theories

TL;DR

This paper demonstrates that the Zamololchikov metric on conformal moduli spaces of four-dimensional superconformal theories is Kahler, using superconformal Ward identities to establish this geometric property.

Contribution

It proves that the natural metric on these moduli spaces is Kahler, providing a geometric insight into the structure of superconformal theories.

Findings

The Zamololchikov metric is Kahler.

Superconformal Ward identities are key to the proof.

The result applies to theories obtained by superpotential deformations.

Abstract

Conformal moduli spaces of four-dimensional superconformal theories obtained by deformations of a superpotential are considered. These spaces possess a natural metric (a Zamolodchikov metric). This metric is shown to be Kahler. The proof is based on superconformal Ward identities.