Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields

Abstract

In this paper, we 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 find that for both the Zn group and the S3 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 find the same scaling for Zn theories. However, there is no generalized free field when the bulk comes from more generic fusion categories such as the Fibonacci model.