Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Four-point functions in the Fortuin-Kasteley cluster model
Speaker: Jesper Jacobsen, École Normale Supérieure
Date: April 14, 2021
Time: 14:30:00 Hours
Venue: AG-77
Abstract: The determination of four-point correlation functions of two-dimensional lattice models is of fundamental importance in statistical physics. In the limit of an infinite lattice, this question can be formulated in terms of conformal field theory (CFT). For the so-called minimal models the problem was solved more than 30 years ago, by using that the existence of singular states implies that the correlation functions must satisfy certain differential equations. This settles the issue for models defined in terms of local degrees of freedom, such as the Ising and 3-state Potts models. However, for geometrical observables in the Fortuin-Kasteleyn cluster formulation of the Q-state Potts model, for generic values of Q, there is in general no locality and no singular states, and so the question remains open. As a warm-up to solving this problem, we discuss which states propagate in the s-channel of such correlation functions, when the four points are brought together two by two. To this end we combine CFT methods with algebraic and numerical approaches to the lattice model. We then outline work in progress that aims at solving the problem entirely, through an interchiral conformal bootstrap setup that makes contact with time-like Liouville field theory and a number of profound algebraic results.
Title of Talk: Four-point functions in the Fortuin-Kasteley cluster model
Speaker: Jesper Jacobsen, École Normale Supérieure
Date: April 14, 2021
Time: 14:30:00 Hours
Venue: AG-77
Abstract: The determination of four-point correlation functions of two-dimensional lattice models is of fundamental importance in statistical physics. In the limit of an infinite lattice, this question can be formulated in terms of conformal field theory (CFT). For the so-called minimal models the problem was solved more than 30 years ago, by using that the existence of singular states implies that the correlation functions must satisfy certain differential equations. This settles the issue for models defined in terms of local degrees of freedom, such as the Ising and 3-state Potts models. However, for geometrical observables in the Fortuin-Kasteleyn cluster formulation of the Q-state Potts model, for generic values of Q, there is in general no locality and no singular states, and so the question remains open. As a warm-up to solving this problem, we discuss which states propagate in the s-channel of such correlation functions, when the four points are brought together two by two. To this end we combine CFT methods with algebraic and numerical approaches to the lattice model. We then outline work in progress that aims at solving the problem entirely, through an interchiral conformal bootstrap setup that makes contact with time-like Liouville field theory and a number of profound algebraic results.