nLab
Verlinde formula

Contents

Idea

Generally, a Verlinde formula gives the dimension of a space of states of Chern-Simons theory for a given gauge group GG. Depending on which one of various different algebraic means to expresses these spaces is used, the Verlinde formula equivalently computes the dimension of spaces of non-abelian theta functions, the dimension of objects in a modular tensor category and so forth.

There are also Verlinde formulas in algebraic geometry (proved by Faltings) and a related one in the theory of vertex operator algebras (proved only in very special cases).

References

See also fusion ring.

A good introduction is in

Dowker, On Verlinde’s formula for the dimensions of vector bundles on moduli spaces, iopscience

A generalization to logarithmic 2d CFTs has been suggested in: