# Conformal blocks, fusion rules and the Verlinde formula

@article{Beauville1994ConformalBF, title={Conformal blocks, fusion rules and the Verlinde formula}, author={Arnaud Beauville}, journal={arXiv: Algebraic Geometry}, year={1994} }

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.

## 12 Citations

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In the Masters Project we give a complete proof of the Factorization theorem in Conformal Field Theory and Local freeness of the sheaf of conformal blocks. We apply these results to give a proof of…

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The main character of these lectures is a finite-dimensional vector space, the space of generalized (or non-Abelian) theta functions, which has recently appeared in (at least) three different…

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We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over Mg;n in terms of tautological classes. The Chern characters of the Verlinde bundles define a…

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We study the birational geometry of the moduli space of parabolic bundles over a projective line, in the framework of Mori’s program. We show that the moduli space is a Mori dream space. As a…

The equivariant Verlinde formula on the moduli of Higgs bundles

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We prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula…

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By exploring the description of chiral blocks in terms of co-invariants, a derivation of the Verlinde formula for WZW models is obtained which is entirely based on the representation theory of affine…

Vertex algebras of CohFT-type

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Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show…

Conformal blocks, Verlinde formula and diagram automorphisms

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THE EQUIVARIANT VERLINDE FORMULA ON THE MODULI OF HIGGS BUNDLES

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We prove an analog of the Verlinde formula on the moduli space of semistable meromorphic G-Higgs bundles over a smooth curve for a reductive group G whose fundamental group is free. The formula…