Yacine Ikhlef, LPTHE (Univ. Paris-6 and CNRS) : Operator algebra in critical loop models and non-rational Conformal Field Theories

Wednesday 5 Oct 2016, 15:00 → 17:00 Europe/Brussels

CYCL08 (Marc de Hemptinne)

Loop models are lattice statistical models with non-local Boltzmann weights, which generally describe extended geometrical objects such as spin interfaces in the Ising model, or percolation clusters. Since the late 80s, they have been recognised as lattice realisations of non-rational Conformal Field Theories (CFTs), with a discrete but infinite spectrum of scaling dimensions. However, the operator algebra of these models is not accessible by the standard methods of CFT. Recently, this question regained interest when Delfino and Viti (2010) showed that the structure constant from the "time-like Liouville" theory gives the correct value for the three-point connectivity of percolation clusters. I will present some related results on the O(n) loop model, including the extension of the Delfino-Viti approach to a large class of scalar operators and the bootstrap analysis for non-scalar operators in CFTs based on the Virasoro and W_3 algebras.