Conformal boundary conditions and three-dimensional topological field theory

TL;DR

A general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies, is presented.

Abstract

We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.

Figures (7)

• Figure 1: Wilson graph for the disk correlators
• Figure 2: $C(S^2;j,j^*)$
• Figure 3: $B(S^2;j,j^*) \,{\otimes}\, B(-S^2;j,j^*)$
• Figure 4: $C(D_a;j)$
• Figure 5: $B(S^2;j,j^*)$