Title: Fusion rules for critical Ising correlations.
Abstract:
Many lattice models of two-dimensional statistical mechanics are
believed to have conformally invariant scaling limits at criticality,
described by Conformal Field Theory. One manifestation of this
phenomenon is that there are random variables ("fields") in these
models that have power-law decay as the lattice mesh goes to zero,
and, when properly rescaled, converge to correlation functions in the
corresponding CFT. In a joint project with D. Chelkak and C. Hongler,
we have proven this result for a natural family of random variables in
the Ising model. As a byproduct, we obtain a description of the CFT
correlation functions in terms of solutions to boundary value
problems. In this talk, I will focus on explaining how this
description leads to a proof of fusion rules for the CFT correlations.
These rules indicate how some of these correlations appear in the
asymptotic expansions of others, naturally reflecting the discrete
picture.