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Solitonic symmetry as non-invertible symmetry: cohomology theories with TQFT coefficients
by Shi Chen, Yuya Tanizaki
Submission summary
Authors (as registered SciPost users): | Shi Chen |
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Preprint Link: | https://arxiv.org/abs/2307.00939v2 (pdf) |
Date submitted: | 2024-04-19 03:43 |
Submitted by: | Chen, Shi |
Submitted to: | SciPost Physics |
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Academic field: | Physics |
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Approach: | Theoretical |
Abstract
Originating from the topology of the path-integral target space $Y$, solitonic symmetry describes the conservation law of topological solitons and the selection rule of defect operators. As Ref.~\cite{Chen:2022cyw} exemplifies, the conventional treatment of solitonic symmetry as an invertible symmetry based on homotopy groups is inappropriate. In this paper, we develop a systematic framework to treat solitonic symmetries as non-invertible generalized symmetries. We propose that the non-invertible solitonic symmetries are generated by the partition functions of auxiliary topological quantum field theories (TQFTs) coupled with the target space $Y$. We then understand solitonic symmetries as non-invertible cohomology theories on $Y$ with TQFT coefficients. This perspective enables us to identify the invertible solitonic subsymmetries and also clarifies the topological origin of the non-invertibility in solitonic symmetry. We finally discuss how solitonic symmetry relies on and goes beyond the conventional wisdom of homotopy groups. This paper is aimed at a tentative general framework for solitonic symmetry, serving as a starting point for future developments.
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