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- W3110776667 abstract "The spectrum of conformal weights for the CFT describing the two-dimensional critical $Q$-state Potts model (or its close cousin, the dense loop model) has been known for more than 30 years. However, the exact nature of the corresponding $hbox{Vir}otimesoverline{hbox{Vir}}$ representations has remained unknown up to now. Here, we solve the problem for generic values of $Q$. This is achieved by a mixture of different techniques: a careful study of Koo--Saleur generators [arXiv:hep-th/9312156], combined with measurements of four-point amplitudes, on the numerical side, and OPEs and the four-point amplitudes recently determined using the interchiral conformal bootstrap in [arXiv:2005.07258] on the analytical side. We find that null-descendants of diagonal fields having weights $(h_{r,1},h_{r,1})$ (with $rin mathbb{N}^*$) are truly zero, so these fields come with simple $hbox{Vir}otimesoverline{hbox{Vir}}$ (Kac) modules. Meanwhile, fields with weights $(h_{r,s},h_{r,-s})$ and $(h_{r,-s},h_{r,s})$ (with $r,sinmathbb{N}^*$) come in indecomposable but not fully reducible representations mixing four simple $hbox{Vir}otimesoverline{hbox{Vir}}$ modules with a familiar diamond shape. The top and bottom fields in these diamonds have weights $(h_{r,-s},h_{r,-s})$, and form a two-dimensional Jordan cell for $L_0$ and $bar{L}_0$. This establishes, among other things, that the Potts-model CFT is logarithmic for $Q$ generic. Unlike the case of non-generic (root of unity) values of $Q$, these indecomposable structures are not present in finite size, but we can nevertheless show from the numerical study of the lattice model how the rank-two Jordan cells build up in the infinite-size limit." @default.
- W3110776667 created "2020-12-21" @default.
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- W3110776667 date "2020-10-01" @default.
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- W3110776667 title "The action of the Virasoro algebra in the two-dimensional Potts and loop models at generic Q" @default.
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- W3110776667 doi "https://doi.org/10.1007/jhep10(2020)109" @default.
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