Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917704921776128 |
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| author | Cao, Weiguang Lu, Xiaochuan Melia, Tom |
| author_facet | Cao, Weiguang Lu, Xiaochuan Melia, Tom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10139 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence Cao, Weiguang Lu, Xiaochuan Melia, Tom High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Phenomenology Representation Theory 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. |
| title | Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Phenomenology Representation Theory |
| url | https://arxiv.org/abs/2312.10139 |