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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
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
https://arxiv.org/abs/2312.10139v2
(pdf)
|
| Date accepted: |
2024-07-09 |
| Date submitted: |
2024-06-27 09:46 |
| Submitted by: |
Melia, Tom |
| Submitted to: |
SciPost Physics Core |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- Condensed Matter Physics - Theory
- High-Energy Physics - Theory
- Statistical and Soft Matter Physics
|
| Approach: |
Theoretical |
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.
