Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields

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 [Formula: see text] group and the [Formula: see text] 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 [Formula: see text] theories. However, there is no generalized free field when the bulk comes from more generic fusion categories such as the Fibonacci model.