Verlinde formula

Generally, a *Verlinde formula* gives the dimension of a space of states of Chern-Simons theory for a given gauge group $G$. 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).

See also fusion ring.

- Gerd Faltings,
*A proof for the Verlinde formula*1994

A good introduction is in

- Shigeru Mukai,
*An introduction to invariants and moduli*, Cambridge Univ. Press 2003

Dowker, *On Verlindeâ€™s formula for the dimensions of vector bundles on moduli spaces*, iopscience

- Juergen Fuchs, Christoph Schweigert,
*A representation theoretic approach to the WZW Verlinde formula*, 1997

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

- Thomas Creutzig, Terry Gannon,
*Logarithmic conformal field theory, log-modular tensor categories and modular forms*, J. Phys. A**50**, 404004 (2017) (doi:10.1088/1751-8121/aa8538, arXiv:1605.04630)