nLab
Bruhat-Tits tree

Contents

Contents

Idea

(…)

Examples

The Bruhat-Tits tree of SL(2)SL(2)

The Bruhat-Tits tree of the special linear group SL(2)SL(2):

graphics from Casselman 14

In the 2-adic AdS/CFT correspondence this tree plays the role of anti de Sitter spacetime. This may be regarded (at some finite depth truncation) as a tree-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?)

References

General

  • Bill Casselman, The Bruhat-Tits tree of SL(2)\mathrm{SL}(2), 2014 (pdf, pdf)

In pp-adic string theory

Suggestion that the disk worldsheet of the open p-adic string is to be identified with the Bruhat-Tits tree T pT_p:

Suggestion to identify the Bruhat-Tits tree T pT_p with anti de Sitter spacetime in the p-adic AdS/CFT correspondence:

  • Steven Gubser, Johannes Knaute, Sarthak Parikh, Andreas Samberg, Przemek Witaszczyk, pp-adic AdS/CFT, Communications in Mathematical Physics volume 352, pages 1019–1059 (2017) (arXiv:1605.01061)

Discussion of Bruhat-Tits-tree tensor networks in this context of the p-adic AdS/CFT correspondence:

  • Arpan Bhattacharyya, Ling-Yan Hung, Yang Lei, Wei Li, Tensor network and (pp-adic) AdS/CFT, JHEP 1801 (2018) 139 (arXiv:1703.05445)

  • Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson, pp-adic CFT is a holographic tensor network (arXiv:1902.01411)

Last revised on February 9, 2020 at 05:40:44. See the history of this page for a list of all contributions to it.