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U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
by Adrien Arbalestrier, Riccardo Argurio, Luigi Tizzano
Submission summary
| Authors (as registered SciPost users): | Riccardo Argurio |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2502.12997v2 (pdf) |
| Date submitted: | 2025-03-26 17:04 |
| Submitted by: | Argurio, Riccardo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these two structures are intertwined. This phenomenon arises in four dimensions when gauging one of multiple $U(1)$ 0-form symmetries in the presence of mixed 't Hooft anomalies. We illustrate this with two distinct models that flow to an IR gapless phase and a gapped phase, respectively, and examine how this symmetry structure manifests in each case. Additionally, we investigate a five-dimensional model where a similar structure exists intrinsically. Our main tool is a symmetry TQFT in one higher dimension, formulated using non-compact gauge fields and having infinitely many topological operators. We carefully determine its boundary conditions and provide a detailed discussion on various dressing choices for its bulk topological operators.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
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Report
The paper investigates the symmetry structures arising in quantum field theories (QFTs) with $U(1)^{(0)}_{\mathsf{A}} \times U(1)^{(0)}_{\mathsf{C}}$ global symmetries characterized by specific 't Hooft anomalies ($k_{\mathsf{A}^3}, k_{\mathsf{A}^2\mathsf{C}}, k_{\mathsf{A}\mathsf{C}^2}, k_{\mathsf{C}^3}$). It focuses specifically on the consequences of gauging the $U(1)^{(0)}_{\mathsf{C}}$ symmetry (assuming $k_{\mathsf{C}^3}=0$), particularly in scenarios where this leads to the simultaneous emergence of higher-group symmetries (mixing 0-form and 1-form symmetries) and non-invertible symmetries. The authors term this combination the generalized Abelian symmetry structure and provide a unified framework for its analysis using the Symmetry Topological Field Theory (SymTFT).
The work details the 5d SymTFT action governing this generalized structure, where the $U(1)^{(0)}_{\mathsf{A}}$ symmetry becomes non-invertible (due to $k_{\mathsf{A}\mathsf{C}^2} \neq 0$) while exhibiting 2-group mixing with the emergent magnetic $U(1)^{(1)}_{\mathsf{C}}$ symmetry (due to $k_{\mathsf{A}^2\mathsf{C}} \neq 0$). It clarifies the behavior of the corresponding bulk SymTFT operators $V_\alpha$ and $T_m$: $V_\alpha$ (related to $U(1)^{(0)}_{\mathsf{A}}$) becomes non-invertible and may require non-genuine descriptions like cylinder attachments, while $T_m$ (related to $U(1)^{(1)}_{\mathsf{C}}$) can often be rendered genuine via stacking with appropriate 2d TQFTs incorporating both anomaly coefficients. Furthermore, the paper analyzes the scheme dependence of anomaly coefficients ($k_{\mathsf{A}^3}, k_{\mathsf{A}^2\mathsf{C}}$) under field redefinitions within the SymTFT, demonstrating how non-invertibility ($k_{\mathsf{A}\mathsf{C}^2} \neq 0$) influences these shifts. The SymTFT framework is also shown to naturally explain the necessity of quantum mechanics dressings for 't Hooft lines in certain phases (e.g., Goldstone-Maxwell) when $k_{\mathsf{A}\mathsf{C}^2} \neq 0$.
The paper is very well-written and clearly presented. It merits publication in SciPost once the following minor points are addressed.
Requested changes
1. In Section 2.4, the authors point out that the presence of a non-invertible symmetry can induce a 2-group coefficient. It would be helpful if the authors could comment on whether this statement also applies to finite discrete symmetries.
2. Minor typos:
2.1 Above Eq. (2.10): as follow: -> as follows:
2.2 Above Eq. (2.61): whose associated edge modes gauge transformation are -> whose associated edge mode gauge transformations are.
2.3 Below Eq. (C.4): These operator are -> These operators are
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Ask for minor revision