Braiding in Conformal Field Theory and Solvable Lattice Models

TL;DR

This paper computes braiding matrices in rational conformal field theory and uses them to construct solvable lattice models with explicit Boltzmann weights, linking conformal blocks to statistical mechanics.

Contribution

It provides a general method to compute braiding matrices for four-point functions and constructs solvable lattice models from these matrices, including explicit Boltzmann weights.

Findings

Braiding matrices for four-point functions are explicitly computed.

Solvable lattice models are constructed from braiding matrices.

Boltzmann weights for height models are derived.

Abstract

Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two block four point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of rational conformal field theory. The braidings of $SU(N)_k$ with the fundamental are evaluated and are used as examples. Solvable interaction round the face lattice models are constructed from these braiding matrices, and their Boltzmann weights are given. This allows, in particular, for the derivation of the Boltzmann weights of such solvable height models.