HEP Theory Journal Club

Tensor network and (p-adic) AdS/CFT

Arpan Bhattacharyya

Fudan University

We will first review connection between tensor network/ AdS/CFT correspondence, emphasizing over the fact that from this approach one can see some aspects of the bulk boundary correspondence naturally emerges. One of the important aspect of the AdS/CFT correspondence is the bulk operator reconstruction (Hamilton-Kabat-Lifschytz-Lowe reconstruction). We will describe how the reconstruction of a bulk operator can be organized systematically using the tensor network approach. With a suitable parameterization, an analogue of the HKLL formula emerges, involving a smearing function satisfying a Klein Gordon equation in the graph. The parameterization also allows us to read off interaction vertices, and build up loop diagrams systematically. When we interpret the Bruhat-Tits tree as a tensor network, we recover (partially) features of the p-adic AdS/CFT dictionary discussed recently in the literature.