Wilson line networks in p-adic AdS/CFT

Abstract

Abstract The p-adic AdS/CFT is a holographic duality based on the p-adic number field ℚ p . For a p-adic CFT living on 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 ℚ p . We propose that bulk theory can be formulated as a lattice gauge theory of PGL(2, 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.

Keywords

• AdS-CFT Correspondence
• Wilson, ’t Hooft and Polyakov loops
• Chern-Simons Theories
• Conformal Field Theory