Moduli Spaces in CFT: Large Charge Operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910192535339008 |
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| author | Cuomo, Gabriel Rastelli, Leonardo Sharon, Adar |
| author_facet | Cuomo, Gabriel Rastelli, Leonardo Sharon, Adar |
| contents | Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is ${\it also}$ broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional ${\cal N}=1$ CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moduli Spaces in CFT: Large Charge Operators Cuomo, Gabriel Rastelli, Leonardo Sharon, Adar High Energy Physics - Theory Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is ${\it also}$ broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional ${\cal N}=1$ CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space. |
| title | Moduli Spaces in CFT: Large Charge Operators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.19441 |