On the Virasoro six-point identity block and chaos
Abstract We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge c and a sparse spectrum, the leading contribution to this correlation function is the six-point Vira...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2020)002 |
| _version_ | 1811224237961117696 |
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| author | Tarek Anous Felix M. Haehl |
| author_facet | Tarek Anous Felix M. Haehl |
| author_sort | Tarek Anous |
| collection | DOAJ |
| description | Abstract We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge c and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block — corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor SL(2, ℝ) (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large c as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks’ relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition. |
| first_indexed | 2024-04-12T08:46:08Z |
| format | Article |
| id | doaj.art-60545e2b1376447c989a85089efdf060 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-12T08:46:08Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-60545e2b1376447c989a85089efdf0602022-12-22T03:39:43ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020813410.1007/JHEP08(2020)002On the Virasoro six-point identity block and chaosTarek Anous0Felix M. Haehl1∆-Institute for Theoretical Physics & Institute for Theoretical Physics, University of AmsterdamSchool of Natural Sciences, Institute for Advanced StudyAbstract We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge c and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block — corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor SL(2, ℝ) (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large c as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks’ relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.http://link.springer.com/article/10.1007/JHEP08(2020)002Conformal Field TheoryAdS-CFT CorrespondenceEffective Field TheoriesStochastic Processes |
| spellingShingle | Tarek Anous Felix M. Haehl On the Virasoro six-point identity block and chaos Journal of High Energy Physics Conformal Field Theory AdS-CFT Correspondence Effective Field Theories Stochastic Processes |
| title | On the Virasoro six-point identity block and chaos |
| title_full | On the Virasoro six-point identity block and chaos |
| title_fullStr | On the Virasoro six-point identity block and chaos |
| title_full_unstemmed | On the Virasoro six-point identity block and chaos |
| title_short | On the Virasoro six-point identity block and chaos |
| title_sort | on the virasoro six point identity block and chaos |
| topic | Conformal Field Theory AdS-CFT Correspondence Effective Field Theories Stochastic Processes |
| url | http://link.springer.com/article/10.1007/JHEP08(2020)002 |
| work_keys_str_mv | AT tarekanous onthevirasorosixpointidentityblockandchaos AT felixmhaehl onthevirasorosixpointidentityblockandchaos |