TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.3.055
TI  - Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence
PY  - 2024/08/14
UR  - https://scipost.org/SciPostPhysCore.7.3.055
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 3
SP  - 055
A1  - Cao, Weiguang
AU  - Lu, Xiaochuan
AU  - Melia, Tom
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.7.3.055,
	title={{Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence}},
	author={Weiguang Cao and Xiaochuan Lu and Tom Melia},
	journal={SciPost Phys. Core},
	volume={7},
	pages={055},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.3.055},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.3.055},
}