Boundary conformal field theory and applications to geometrical critical phenomena.
by
Jesper Jacobsen(LPT, ENS)
→
Europe/Stockholm
FA31
FA31
Description
We discuss how techniques from conformal field theory can produce
exact information about two-dimensional geometrical models, such as
percolation and lattice polymers, at the critical point. We then
address more specifically the issue of conformally invariant
boundary conditions (CIBC). While such CIBC have been extensively
classified for unitary models, the geometrical theories of interest here
are in general non-unitary. We provide several examples of new, infinite
families of non-unitary CIBC, formulated in purely geometrical terms. The
corresponding critical exponents are obtained exactly. Building on this,
we compute exactly various crossing probabilities, boundary entropies, and
partition functions in the continuum limit. As a specific application, we
deduce the phase diagram of the O(N) model with boundary anisotropy.
