MS Seminar (Mathematics - String Theory)

Speaker: David Ridout (Australian National U)
Title: A (Working) Verlinde Formula for Fractional Level WZW Models
Date (JST): Tue, Apr 09, 2013, 13:15 - 14:45
Place: Seminar Room A
Abstract: WZW models at admissible levels date back to the late 80's where it was discovered that the characters of certain highest weight representations carry a finite-dimensional representation of the modular group. However, a naive application of the Verlinde formula leads to negative integer "fusion coefficients" in addition to the expected positive integer ones. The resolution of this negative coefficient puzzle arrived only in 2008, utilising methods developed to understand examples of logarithmic CFTs. However, the question of obtaining a working Verlinde formula remained.

Since then, we have proposed (with Thomas Creutzig) a rather general formalism for computing various properties of a certain class of logarithmic theories. In this talk, I will explain how this formalism completely solves the 25 year old problem of obtaining positive integer Verlinde coefficients for admissible level SL(2;R) WZW models. We are confident that the analogous problems for other groups will have the same solutions, though there are considerable technicalities to be overcome in demonstrating this.