general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
A version of the AdS/CFT correspondence (specifically: AdS3/CFT2 duality) for p-adic physics, obtained by passing on the conformal field theory-side from the complex geometry, hence (via GAGA)algebraic geometry of 2d CFT to arithmetic geometry over p-adic numbers, and on the string theory-side to p-adic string theory (?)
Here the arithmetic geometry-version of the bulk AdS spacetime is identified with the Bruhat-Tits tree for the projective general linear group $PGL(2,\mathbb{Q}_p)$:
graphics from Casselman 14
This may be regarded (at some finite depth truncation) as a tensor network state:
graphics from Sati-Schreiber 19c
(As in HMSS 16, HLM 19. But maybe one wants the Poincaré-dual networks, instead, as in HMPS 18?)
There is the suggestion that BTZ black holes are encoded by networks that look like Bruhat-Tits trees towards the boundaries and like matrix product states towards the interior:
(As in ESZ 19.)
Suggestion to identify the Bruhat-Tits tree $T_p$ with anti de Sitter spacetime in the p-adic AdS/CFT correspondence:
Steven Gubser, Johannes Knaute, Sarthak Parikh, Andreas Samberg, Przemek Witaszczyk, $p$-adic AdS/CFT, Communications in Mathematical Physics volume 352, pages 1019–1059 (2017) (arXiv:1605.01061)
Steven Gubser, Sarthak Parikh, Geodesic bulk diagrams on the Bruhat-Tits tree (arXiv:1704.01149)
Relation to tensor networks:
Matthew Heydeman, Matilde Marcolli, Ingmar Saberi, Bogdan Stoica, Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the $AdS_3/CFT_2$ correspondence (arXiv:1605.07639)
Arpan Bhattacharyya, Ling-Yan Hung, Yang Lei, Wei Li, Tensor network and ($p$-adic) AdS/CFT, JHEP 1801 (2018) 139 (arXiv:1703.05445)
Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson, $p$-adic CFT is a holographic tensor network (arXiv:1902.01411)
Including spinors:
Including BTZ black holes:
Matthew Heydeman, Matilde Marcolli, Sarthak Parikh, Ingmar Saberi, Nonarchimedean Holographic Entropy from Networks of Perfect Tensors (arXiv:1812.04057)
Stephen Ebert, Hao-Yu Sun, Meng-Yang Zhang, Probing holography in $p$-adic CFT (arXiv:1911.06313)
An expository account is given in
Proposed realization of aspects of p-adic AdS/CFT correspondence in solid-state physics:
Last revised on February 9, 2020 at 05:36:39. See the history of this page for a list of all contributions to it.