Abstract
The fully packed loop (FPL) model is a statistical model related to the integrable 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 W3 symmetry in the continuum. The partition function on the torus is calculated exactly, yielding new modular invariants of W3 characters. The full conformal field theory spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.
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