Antti Kupiainen – University of Helsinki
Wednesday, April 2nd , 10:45AM DST
Wess-Zumino-Witten models and path integrals
The Wess-Zumino-Witten (WZW) model is a 2 dimensional conformal field theory (CFT) . In this talk I will review the basic facts about the path integral formulation of WZW models and then discuss the coset theory SL(2,C)/SU(2). This theory can be formulated in terms of field taking values in the 3-dimensional hyperbolic space and it has been studied as one of the simplest realisations of the AdS/CFT correspondence. By the work of Ribault, Teschner, Hikida and Schomerus it has also been argued to have a mapping to the Liouville CFT which is the basic building block of two dimensional quantum gravity and random surface theory. I will explain how this theory can be constructed probabilistically using the theory of Gaussian Multiplicative Chaos and how in a very general setup the correlation functions of its primary fields can be mapped to those of the Liouville CFT.