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arXiv · 2511.22647

Tensor complex renormalization with generalized symmetry and topological bootstrap

Dong-Yu Bao·Gong Cheng·Hong-Hao Song·Zheng-Cheng Gu
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Abstract

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.

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Dong-Yu Bao, Gong Cheng, Hong-Hao Song, Zheng-Cheng Gu. 2025-11-27. Tensor complex renormalization with generalized symmetry and topological bootstrap. https://arxiv.org/abs/2511.22647

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