Tensor complex renormalization with generalized symmetry and topological bootstrap

Fuente: arXiv
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Main Authors: Bao, Dong-Yu, Cheng, Gong, Song, Hong-Hao, Gu, Zheng-Cheng
Format: Preprint
Published: 2025
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_version_ 1866914173565272064
author Bao, Dong-Yu
Cheng, Gong
Song, Hong-Hao
Gu, Zheng-Cheng
author_facet Bao, Dong-Yu
Cheng, Gong
Song, Hong-Hao
Gu, Zheng-Cheng
contents Recent progress in generalized symmetry and topological holography has shown that, in conformal field theory (CFT), topological data from one dimensional higher can play a key role in determining local dynamics. Based on this insight, a fixed-point (FP) tensor complex (TC) for CFT has recently been constructed. In this work, we develop a TC renormalization (TCR) algorithm adapted to this CFT-based structure, forming a renormalization-group (RG) framework with generalized symmetry. We show that the full FP tensor can emerge from the RG flow starting with only the three-point function of the primary fields. Remarkably, even when starting solely from topological data, the RG process can still reconstruct the full FP tensor--a method we call as topological bootstrap. This approach deepens the connection between the topological and dynamical aspects of CFT and suggests pathways toward a fully algebraic description of gapless quantum states, with potential extensions to higher dimensions.
format Preprint
id arxiv_https___arxiv_org_abs_2511_22647
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tensor complex renormalization with generalized symmetry and topological bootstrap
Bao, Dong-Yu
Cheng, Gong
Song, Hong-Hao
Gu, Zheng-Cheng
Strongly Correlated Electrons
Mathematical Physics
Recent progress in generalized symmetry and topological holography has shown that, in conformal field theory (CFT), topological data from one dimensional higher can play a key role in determining local dynamics. Based on this insight, a fixed-point (FP) tensor complex (TC) for CFT has recently been constructed. In this work, we develop a TC renormalization (TCR) algorithm adapted to this CFT-based structure, forming a renormalization-group (RG) framework with generalized symmetry. We show that the full FP tensor can emerge from the RG flow starting with only the three-point function of the primary fields. Remarkably, even when starting solely from topological data, the RG process can still reconstruct the full FP tensor--a method we call as topological bootstrap. This approach deepens the connection between the topological and dynamical aspects of CFT and suggests pathways toward a fully algebraic description of gapless quantum states, with potential extensions to higher dimensions.
title Tensor complex renormalization with generalized symmetry and topological bootstrap
topic Strongly Correlated Electrons
Mathematical Physics
url https://arxiv.org/abs/2511.22647