Asato Tsuchiya - Renormalization group and quantum error correction

This talk was part of the Workshop on "Large-N Matrix Models and Emergent Geometry" held at the ESI September 4 — 8, 2023.

Tensor network models (MERA, HaPPY code, random tensor network, etc.) are considered as giving networks that can be interpreted as discrete bulk geometry emerging from a boundary theory through quantum entanglement. It is needed to construct a continuum analog of tensor network to obtain continuum bulk geometry. The scale dependence of a wave functional is expected to give such a continuum network. It has also been discussed that quantum error correction plays a crucial role in the correspondence between bulk and boundary. In this talk, we derive an exact renormalization group equation that can determine the scale dependence of wave functionals and discuss the structure of quantum error correction in continuum networks.