Is there a known case of some kind of many-body lattice system which in the continuum limit is described by a conformal field theory with an irrational central charge? If not, is it likely to exist?
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$\begingroup$ See parallels between Liouville and XXZ - Faddeev $\endgroup$– AHusainJun 26, 2017 at 15:43
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This may depend on what you mean by a "many-body lattice system". It has recently been shown that conformal loop ensembles are described by a 2d CFT (Liouville theory) whose central charge can take any value in $(-\infty, 1)$.
Before that, it was known how to formulate the Potts model with arbitrary (i.e. non-integer) values of the number of states, and this number of states corresponds to the central charge of the relevant CFT. But that CFT is not known. As far as I understand, the Liouville theory that describes conformal loop ensembles could be a sector of that CFT.
