Coupled minimal models revisited II: Constraints from permutation symmetry

Leite Antunes, António; Behan, Connor

Preprint

PUBDB-2025-05185

Coupled minimal models revisited II: Constraints from permutation symmetry

Leite Antunes, A. (Corresponding author)DESY* ; Behan, C.

2025

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Report No.: arXiv:2412.21107

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 vacuum. In this paper, we build on the construction of [A. Antunes and C. Behan, Phys. Rev. Lett. 130, 071602 (2023)], 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 [A. Antunes and C. Behan, Phys. Rev. Lett. 130, 071602 (2023)], some of which can exist for smaller values of the UV central charge.

Classification:

ddc:530

Note: SciPost Phys. 18, 132 (2025). 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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