Tensor network and (\(p\)-adic) AdS/CFT

Abstract

The tensor network/geometry correspondence is a proposed discrete version of the holographic duality. We show how important features in the AdS/CFT dictionary, such as the bulk operator reconstruction via the HKLL relation and the map between bulk isometry and boundary global symmetry, can emerge naturally from the tensor network construction. Furthermore, we propose that the tensor network living on the Bruhat-Tits tree gives a concrete realization of the recently proposed \(p\)-adic AdS/CFT (a holographic duality based on the \(p\)-adic number field \(\mathbb{Q}_p\)); in particular, the wavefunction of the tensor network defines the ground state of the boundary \(p\)-adic CFT.