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

Weiguang Cao, Xiaochuan Lu, Tom Melia

SciPost Phys. Core 7, 055 (2024) · published 14 August 2024

- doi: 10.21468/SciPostPhysCore.7.3.055
- Submissions/Reports

### 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.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Weiguang Cao, -
^{3}Xiaochuan Lu, -
^{2}Tom Melia

^{1}東京大学 / University of Tokyo [UT]^{2}Kavli Institute for the Physics and Mathematics of the Universe [IPMU]^{3}University of California, San Diego [UCSD]