The fully packed loop model as a non-rational $W_3$ conformal field theory

Abstract

The fully packed loop (FPL) model is a statistical model related to the integrable $U_q({\widehat{\mathfrak{sl}}}_3)$ vertex model. In this paper we study the continuum limit of the FPL. With the appropriate weight of non-contractible loops, we give evidence of an extended $W_3$ symmetry in the continuum. The partition function on the torus is calculated exactly, yielding new modular invariants of $W_3$ characters. The full CFT spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.

27 pages, 16 figures

References in corpus (4)

• Correlation functions in conformal Toda field theory I
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Correlation functions in loop models
• Integrability and conformal data of the dimer model

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• The imaginary Toda field theory
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