A note on ensemble holography for rational tori
Abstract We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theori...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2021)177 |
| _version_ | 1819176572890906624 |
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| author | Joris Raeymaekers |
| author_facet | Joris Raeymaekers |
| author_sort | Joris Raeymaekers |
| collection | DOAJ |
| description | Abstract We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the non-primitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants. These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact U(1) × U(1) Chern-Simons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS3 leads to the vacuum character of the chiral algebra. We also comment on wormhole-like contributions to the multi-boundary path integral. |
| first_indexed | 2024-12-22T21:12:54Z |
| format | Article |
| id | doaj.art-1df078ef41384d89ae64dba586639f40 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T21:12:54Z |
| publishDate | 2021-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1df078ef41384d89ae64dba586639f402022-12-21T18:12:27ZengSpringerOpenJournal of High Energy Physics1029-84792021-12-0120211212710.1007/JHEP12(2021)177A note on ensemble holography for rational toriJoris Raeymaekers0CEICO, Institute of Physics of the Czech Academy of SciencesAbstract We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the non-primitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants. These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact U(1) × U(1) Chern-Simons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS3 leads to the vacuum character of the chiral algebra. We also comment on wormhole-like contributions to the multi-boundary path integral.https://doi.org/10.1007/JHEP12(2021)177AdS-CFT CorrespondenceConformal Field TheoryModels of Quantum Gravity |
| spellingShingle | Joris Raeymaekers A note on ensemble holography for rational tori Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory Models of Quantum Gravity |
| title | A note on ensemble holography for rational tori |
| title_full | A note on ensemble holography for rational tori |
| title_fullStr | A note on ensemble holography for rational tori |
| title_full_unstemmed | A note on ensemble holography for rational tori |
| title_short | A note on ensemble holography for rational tori |
| title_sort | note on ensemble holography for rational tori |
| topic | AdS-CFT Correspondence Conformal Field Theory Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP12(2021)177 |
| work_keys_str_mv | AT jorisraeymaekers anoteonensembleholographyforrationaltori AT jorisraeymaekers noteonensembleholographyforrationaltori |