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Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
by Lakshya Bhardwaj, Sakura Schafer-Nameki
Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj |
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| Preprint Link: | https://arxiv.org/abs/2305.17159v3 (pdf) |
| Date accepted: | Sept. 15, 2025 |
| Date submitted: | Aug. 28, 2025, 1:10 p.m. |
| Submitted by: | Lakshya Bhardwaj |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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Abstract
Consider a d-dimensional quantum field theory (QFT) $\mathfrak{T}$, with a generalized symmetry $\mathcal{S}$, which may or may not be invertible. We study the action of $\mathcal{S}$ on generalized or $q$-charges, i.e. $q$-dimensional operators. The main result of this paper is that $q$-charges are characterized in terms of the topological defects of the Symmetry Topological Field Theory (SymTFT) of $\mathcal{S}$, also known as the ``Sandwich Construction''. The SymTFT is a $(d+1)$-dimensional topological field theory, which encodes the symmetry $\mathcal{S}$ and the physical theory in terms of its boundary conditions. Our proposal applies quite generally to any finite symmetry $\mathcal{S}$, including non-invertible, categorical symmetries. Mathematically, the topological defects of the SymTFT form the Drinfeld Center of the symmetry category $\mathcal{S}$. Applied to invertible symmetries, we recover the result of Part I of this series of papers. After providing general arguments for the identification of $q$-charges with the topological defects of the SymTFT, we develop this program in detail for QFTs in 2d (for general fusion category symmetries) and 3d (for fusion 2-category symmetries).
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Author comments upon resubmission
We have made the modifications based on their suggestions and hope that the paper would now be fit for publication. Please let us know if further modifications are needed.
For referee 2:
We have clarified why we don't study (d-1) charges in footnote in Statement 3.2.
For referee 1:
(1) We have added some citations at the beginning of section 3.2.
(2) We have modified the sentence with appropriate citation.
(3) Thank you, we have modified the equations.
Typos have also been corrected. Thank you.
Published as SciPost Phys. 19, 098 (2025)