Diagonal fields in critical loop models

Abstract

In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose 3-point functions coincide with those of Liouville theory at c≤ 1. We study their N-point functions, which depend on the 2^{N-1} weights of topologically inequivalent loops on a sphere with N punctures. Using a numerical conformal bootstrap approach, we find that 4-point functions decompose into infinite but discrete linear combinations of conformal blocks. We conclude that diagonal fields belong to an extension of the O(n) model.