nLab
Verlinde formula

Contents

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

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

Dowker, On Verlinde’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 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

Last revised on October 19, 2019 at 14:52:14. See the history of this page for a list of all contributions to it.