Orateur
Steven Flores
(University of Helsinki)
Description
If a c ≤ 1 conformal field theory (CFT) correlation function contains a primary field whose conformal weight follows from the Kac formula, then the correlation function obeys a certain BPZ partial differential equation (PDE). Furthermore, if its weight belongs to the (1,2) or (2,1) position of the Kac grid, then the associated BPZ equation is a second-order linear homogeneous PDE. In this talk, we consider the system of 2N such BPZ equations and three conformal Ward identities that govern a CFT boundary correlation function exclusively of 2N (1, 2) or (2, 1) primary fields. We rigorously show that the dimension of the solution space for this system is CN, the Nth Catalan number, and that the CFT Coulomb gas formalism gives explicit formulas for all of its solutions. Then we use these results to prove the existence and uniqueness (up to a constant multiple) of a monodromy-invariant CFT bulk correlation function of 2N (1,2) or (2,1) primary fields. Furthermore, we determine an explicit formula for this correlation function. This is joint work with Peter Kleban (University of Maine), Jacob Simmons (Maine Maritime Academy), Eveliina Peltola (University of Helsinki), and Robert Ziff (University of Michigan).
Auteur principal
Steven Flores
(University of Helsinki)
