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arXiv · 1812.06059

Wilson line networks in $p$-adic AdS/CFT

Ling-Yan Hung·Wei Li·Charles M. Melby-Thompson
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Abstract

The $p$-adic AdS/CFT is a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$. For a $p$-adic CFT living on $\mathbb{Q}_p$ and with complex-valued fields, the bulk theory is defined on the Bruhat-Tits tree, which can be viewed as the bulk dual of $\mathbb{Q}_p$. We propose that bulk theory can be formulated as a lattice gauge theory of PGL$(2,\mathbb{Q}_p)$ on the Bruhat-Tits tree, and show that the Wilson line networks in this lattice gauge theory can reproduce all the correlation functions of the boundary $p$-adic CFT.

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Ling-Yan Hung, Wei Li, Charles M. Melby-Thompson. 2018-12-14. Wilson line networks in $p$-adic AdS/CFT. https://doi.org/10.1007/jhep05(2019)118

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