16680 2102.12024 10.1007/JHEP09(2021)097 97 97 Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree Regular Article - Theoretical Physics 1 32 2021 9 16 2021 3 9 2021 8 6 2021 8 14 2021 9 16 The Author(s) 2021 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2021 2021 9 9 Lin Chen linchen91@pku.edu.cn Xirong Liu 20210190003@fudan.edu.cn Ling-Yan Hung elektron.janethung@gmail.com grid.8547.e 0000 0001 0125 2443 State Key Laboratory of Surface Physics Fudan University Shanghai 200433 China Shanghai Qi Zhi Institute 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District Shanghai 200232 China grid.8547.e 0000 0001 0125 2443 Department of Physics and Center for Field Theory and Particle Physics Fudan University Shanghai 200433 China grid.8547.e 0000 0001 0125 2443 Institute for Nanoelectronic devices and Quantum computing Fudan University Shanghai 200433 China 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. Keywords AdS-CFT Correspondence Black Holes Gauge-gravity correspondence Conformal Field Theory ArXiv ePrint: 2102.12024