For $G$ a suitable Lie group, the Verlinde ring is the collection of isomorphism classes of positive energy representations of the corresponding loop group, equipped with the “fusion” tensor product.
The Verlinde ring is also understood as being the ring of equivariant twisted K-theory classes on $G$ (FHT) and, essentially equivalently, of Chan-Paton gauge fields over D-branes in the WZW model (see there for further references).
Due to
We study conformal field theories with a finite number of primary fields with respect to some chiral algebra. It is shown that the fusion rules are completely determined by the behavior of the characters under the modular group. We illustrate with some examples that conversely the modular properties of the characters can be derived from the fusion rules. We propose how these results can be used to find restrictions on the values of the central charge and conformal dimensions.
See also
Domenico Fiorenza, Alessandro Valentino, $(3,2,1)$-TQFTs and Verlinde algebras (MO question, MO answer)
Dan Freed, Mike Hopkins, Constantin Teleman, Loop Groups and Twisted K-Theory
Wikipedia, Verlinde algebra
Last revised on October 19, 2019 at 14:15:46. See the history of this page for a list of all contributions to it.