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arXiv · 2309.03178

Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields

Xiangdong Zeng·Ling-Yan Hung
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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.

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Xiangdong Zeng, Ling-Yan Hung. 2023-09-06. Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields. https://doi.org/10.3390/e25111543

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