Verlinde formula for chiral homology

In two-dimensional conformal field theory, local holomorphic observables can be modeled by vertex operator algebras. Their global counterparts, the spaces of conformal blocks, form a twisted D-module over the moduli space of smooth curves. In certain cases, conformal blocks are known to extend to stable curves in such a way that they satisfy a gluing formula relating the conformal blocks of a nodal curve to those of its normalization. When these D-modules are flat connections, this reduces the computation of their rank to the genus-zero case, leading to the famous Verlinde formula. I will describe a geometric implementation of these ideas in the language of Beilinson and Drinfeld’s chiral and factorization algebras. In particular, this framework yields a gluing formula for the derived enhancement of conformal blocks given by chiral homology.