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Xiangdong Zeng1,2, Ling-Yan Hung1,2,3,4,5

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Entropy (Basel, Switzerland)
|November 24, 2023
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Summary

We investigated holographic tensor networks and found that the number of generalized free fields in 2D and 3D bulk theories scales with the group order for Zn and S3 groups. This scaling was not observed in more generic fusion categories like the Fibonacci model.

Keywords:
bulk operator reconstructiontensor networktopological field theory

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Condensed Matter Theory

Background:

  • Holographic tensor networks provide a framework for studying quantum field theories.
  • Renormalization group (RG) flows describe how physical systems change with scale.
  • Operator reconstruction is key to understanding the relationship between bulk and boundary theories in holography.

Purpose of the Study:

  • To analyze operator reconstruction within holographic tensor networks describing RG flows.
  • To investigate the scaling of bulk operators in 2D and 3D holographic models.
  • To compare findings across different group structures (Zn, S3) and fusion categories (Fibonacci).

Main Methods:

  • Construction of 2D bulk holographic tensor networks using Dijkgraaf-Witten theories.
  • Analysis of operator scaling behavior for generalized free fields.
  • Generalization of the study to 3D bulk holographic tensor networks.
  • Examination of operator properties in generic fusion categories.

Main Results:

  • In 2D bulk holographic tensor networks (Zn and S3 groups), the number of bulk operators behaving as generalized free fields scales directly with the order of the group.
  • This same scaling behavior was observed in 3D bulk Zn theories.
  • Generalized free fields were not found when the bulk originated from more generic fusion categories, such as the Fibonacci model.

Conclusions:

  • The order of the symmetry group is a critical factor in determining the number of generalized free fields in holographic tensor network models.
  • The findings highlight differences in operator behavior between group-based and more generic fusion category-based holographic constructions.
  • This research contributes to understanding the intricate relationship between symmetry, bulk operators, and RG flows in holographic contexts.