Conformal blocks, fusion rules and the Verlinde formula

TL;DR

This paper rigorously establishes the Verlinde formula for the WZW model, connecting conformal blocks, vector bundle moduli spaces, and determinant line bundles in rational conformal field theory.

Contribution

It provides a rigorous proof of the Verlinde formula for the WZW model, linking conformal blocks to moduli space geometry and determinant line bundles.

Findings

Verlinde formula proven rigorously for WZW model

Dimension of conformal blocks linked to moduli space sections

Results connect conformal field theory with algebraic geometry

Abstract

The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one particular such theory, the WZW model. Thanks to the results of [B-L], [F] and [T-U-Y], this gives the dimension of the space of global sections of the determinant line bundles (and its multiples) on the moduli space of vector bundles with fixed rank and determinant.