Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields

Abstract

In this paper, we would like to study operator reconstruction in a class of holographic tensor networks describing renormalization group flows studied in arXiv:2210.12127. We study examples of 2d bulk holographic tensor networks constructed from Dijkgraaf-Witten theories and found that for both ${\mathbb{Z}}_n$ group and $S_3$ group the number of bulk operators behaving like a generalized free field in the bulk scales as the order of the group. We also generalize our study to 3d bulks and found the same scaling for ${\mathbb{Z}}_n$ theories. However, there is no generalized free field when the bulk comes from more generic fusion categories such as the Fibonacci model.

11 pages, 3 figures