The fully packed loop model as a non-rational W 3 conformal field theory
Résumé
The fully packed loop (FPL) model is a statistical model related to the integrable ${{U}_{q}}\left({{\widehat{\mathfrak{s}\mathfrak{l}}}_{3}}\right)$ 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 conformal field theory spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.