The Fully Packed Loop Model as a Non-Rational W3 Conformal Field Theory. Dupic, T., Estienne, B., & Ikhlef, Y. Journal of Physics A: Mathematical and Theoretical, June, 2016.
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The fully packed loop (FPL) model is a statistical model related to the integrable $U_q(\ hat\{\ mathfrak\{sl\}\}_3)$ 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.
@article{dupicFullyPackedLoop2016a,
  title = {The Fully Packed Loop Model as a Non-Rational {{W3}} Conformal Field Theory},
  author = {Dupic, Thomas and Estienne, Beno{\^i}t and Ikhlef, Yacine},
  year = {2016},
  month = jun,
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {49},
  doi = {10.1088/1751-8113/49/50/505202},
  abstract = {The fully packed loop (FPL) model is a statistical model related to the integrable \$U\_q(\textbackslash hat\{\textbackslash 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.},
}

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