Coupled minimal models revisited II: Constraints from permutation symmetry

TL;DR

This paper investigates the properties of coupled minimal models with permutation symmetry, revealing constraints on conserved currents, spectrum characteristics, and non-invertible symmetries, thereby enriching the understanding of these 2D conformal field theories.

Contribution

It demonstrates that for spins less than 10, additional currents in non-trivial permutation representations are not conserved at IR fixed points, and explores spectrum and symmetry properties of these models.

Findings

Additional currents are not conserved for spins less than 10.

The spectrum of theories exhibits specific properties, especially for N=4.

Non-invertible symmetries impose constraints on the models.

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.