# 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.

## Key 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.