Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree
Abstract In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel “exponential function” on the p-adic numbers that is hinted by t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2021)097 |
| _version_ | 1818643127090544640 |
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| author | Lin Chen Xirong Liu Ling-Yan Hung |
| author_facet | Lin Chen Xirong Liu Ling-Yan Hung |
| author_sort | Lin Chen |
| collection | DOAJ |
| description | Abstract In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel “exponential function” on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL(2, Q p ) Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the p-adic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the “pure” Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree. |
| first_indexed | 2024-12-16T23:54:00Z |
| format | Article |
| id | doaj.art-e53b29e33a1144709244d19662bf68f7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T23:54:00Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e53b29e33a1144709244d19662bf68f72022-12-21T22:11:16ZengSpringerOpenJournal of High Energy Physics1029-84792021-09-012021913210.1007/JHEP09(2021)097Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits treeLin Chen0Xirong Liu1Ling-Yan Hung2State Key Laboratory of Surface Physics, Fudan UniversityState Key Laboratory of Surface Physics, Fudan UniversityState Key Laboratory of Surface Physics, Fudan UniversityAbstract In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel “exponential function” on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL(2, Q p ) Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the p-adic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the “pure” Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree.https://doi.org/10.1007/JHEP09(2021)097AdS-CFT CorrespondenceBlack HolesGauge-gravity correspondenceConformal Field Theory |
| spellingShingle | Lin Chen Xirong Liu Ling-Yan Hung Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree Journal of High Energy Physics AdS-CFT Correspondence Black Holes Gauge-gravity correspondence Conformal Field Theory |
| title | Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree |
| title_full | Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree |
| title_fullStr | Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree |
| title_full_unstemmed | Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree |
| title_short | Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree |
| title_sort | bending the bruhat tits tree part ii the p adic btz black hole and local diffeomorphism on the bruhat tits tree |
| topic | AdS-CFT Correspondence Black Holes Gauge-gravity correspondence Conformal Field Theory |
| url | https://doi.org/10.1007/JHEP09(2021)097 |
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