Starts 5 Jun 2012 12:30
Ends 5 Jun 2012 20:00
Central European Time
ICTP
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11 I - 34151 Trieste (Italy)
Consider the clusters of same-sign spins in the Ising model. In the scaling limit at criticality, their boundaries become (countably) infinitely many loops that don't intersect, and the Boltzman weight becomes a probability measure for these loop configurations. Conformal loop ensemble (CLE) is a one-parameter family of measures on such loop configurations with properties of locality and conformal invariance. It includes the measure obtained from the scaling limit of the critical Ising model, but also measures corresponding to all central charges between 0 and 1. It is believed that this loop description contains all the information of the usual local-operator CFT, in particular about minimal models. In this talk I will tell you how to represent the stress tensor and some of its descendants as random variables in CLE. The random variables essentially measure how likely it is that loops be separated by some specific closed curves that look like stars (with a bit of imagination); these stars are made to "rotate" at various angular velocities. It is interesting that the star-figure random variables in principle give definitions for the associated stress-tensor descendants even beyond CFT. This talk will be very elementary: I'll introduce all necessary notions, and if time permits I will give you an idea of how the proof works.
  • M. Poropat