Finiteness of volume of moduli spaces

TL;DR

This paper provides a physics-based proof that certain moduli spaces in conformal field theories have finite volume under the Zamolodchikov metric, confirming a conjecture from 2005 through an RG flow approach.

Contribution

It offers the first physics proof of the finiteness of volume for these moduli spaces, using an RG flow argument to establish the conjecture.

Findings

Confirmed the finiteness of moduli space volume in specific conformal field theories.

Introduced an RG flow method to prove geometric properties of moduli spaces.

Validated a conjecture made at Strings 2005 regarding moduli space volume.

Abstract

We give a ``physics proof'' of a conjecture made by the first author at Strings 2005, that the moduli spaces of certain conformal field theories are finite volume in the Zamolodchikov metric, using an RG flow argument.