Coupled minimal models revisited II: Constraints from permutation symmetry

Abstract

Coupling $N$ large $m$ minimal models and flowing to IR fixed points is a systematic way to build new classes of compact unitary 2d CFTs which are likely to be irrational, and potentially have a positive Virasoro twist gap above the vaccuum. In this paper, we build on the construction of [1], establishing that, for spins less than 10, additional currents transforming in non-trivial irreducible representations of the permutation symmetry $S_N$ are not conserved at the IR fixed points. Along the way, we develop a finer understanding of the spectrum of these theories, of the special properties of the $N=4$ case and of non-invertible symmetries that constrain them. We also discuss variations of the original setup of [1] some of which can exist for smaller values of the UV central charge.

35 pages + references, 3 figures, 13 tables; v2: added references, fixed typo, v3: more discussion and code, v4: clarifications, v5: published version

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Cited by in corpus (4)

• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Minimal Models RG flows: non-invertible symmetries & non-perturbative description
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations