“Irrational CFTs from coupled anyon chains?” by António Antunes, LPENS Paris

Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. In this talk, I will discuss a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N ≥ 3 golden anyon chains together, preserving N copies of the Fibonacci non-invertible symmetry. I will briefly describe the N=2 case, where a weakly first-order phase transition (previously misidentified as an irrational CFT) occurs and some non-trivial (but rational) CFTs appear as unstable fixed points. For N = 3 we will show that a short RG flow occurs towards a stable CFT in the infrared with c~2.09. We indirectly argue that the CFT is irrational by comparing with a list of known rational CFTs with similar central charge. We will end with a discussion of other approaches that could be used to confirm/disprove our claim.