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Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence

by Weiguang Cao, Xiaochuan Lu, Tom Melia

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Authors (as registered SciPost users):

Weiguang Cao · Tom Melia

Abstract

We identify constraints in the energy spectra of quantum theories that have a global $O(N)$ symmetry, where $N$ is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of $N$ in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as $N$ approaches a certain integer, with both states disappearing at precisely integer $N$ and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of $O(N)$ and hold non-perturbatively. We give examples in the spectra of the critical $O(N)$ model.