nLab
Verlinde ring

Contents

Contents

Idea

For GG 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 GG (FHT) and, essentially equivalently, of Chan-Paton gauge fields over D-branes in the WZW model.

References

General

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

Relation to twisted ad-equivariant K-theory

On twisted ad-equivariant K-theory of compact Lie groups and the identification with the Verlinde ring of positive energy representations of their loop group:

Review:

Last revised on March 10, 2021 at 04:42:35. See the history of this page for a list of all contributions to it.