The fully packed loop model as a non-rational W 3 conformal field theory

Source abstract

Abstract The fully packed loop (FPL) model is a statistical model related to the integrable U q ( s l ^ 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 conformal field theory spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.