Half-Spacetime Gauging of 2-Group Symmetry in 3d

Davide Bason, Lorenzo Ruggeri, Wei Cui

Authors on Pith no claims yet

Pith reviewed 2026-05-08 07:44 UTC · model grok-4.3

classification ✦ hep-th

keywords non-invertible symmetries2-group symmetryduality defectshalf-spacetime gaugingmixed anomalies3d quantum field theorydiscrete gauge symmetry

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The pith

Half-spacetime gauging of a 2-group symmetry in (2+1)d theories produces non-invertible duality defects with explicit fusion rules.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to generate non-invertible duality defects by gauging only half of spacetime in three-dimensional quantum field theories that possess 2-group symmetries. It begins with a parent theory containing two or three discrete Abelian 0-form symmetries that carry a mixed anomaly of a specific cyclic form. Gauging one symmetry factor yields a theory with an intact 2-group symmetry, while gauging another factor produces a theory whose 0-form symmetry is non-invertible. When the parent theory has three symmetries arranged in a cycle of anomalies, the different gauging choices generate mutually dual theories whose relation is implemented by the non-invertible defect. The authors derive the fusion rules of these defects and illustrate the construction with concrete examples such as U(1)^3 gauge theories.

Core claim

Starting from a parent theory with two discrete Abelian 0-form symmetries and a prescribed mixed anomaly, gauging one factor produces a theory with a 2-group symmetry while gauging the other yields a theory with a non-invertible 0-form symmetry. When the parent theory possesses three such symmetries with a cyclic anomaly structure, gauging different factors produces mutually dual theories, and the half-spacetime gauging of the 2-group is implemented by a non-invertible duality defect whose fusion rules are obtained explicitly.

What carries the argument

The half-spacetime gauging operation applied to a 2-group symmetry, which acts as a non-invertible duality defect that maps between the different gauged theories and whose fusion rules are computed from the parent anomaly data.

Load-bearing premise

The parent theory must possess two or three discrete Abelian 0-form symmetries carrying a specific mixed anomaly that permits the half-spacetime gauging to produce either a 2-group symmetry or a non-invertible symmetry as described.

What would settle it

A lattice model or numerical simulation of the U(1)×U(1)×U(1) gauge theory example in which the fusion product of two duality defects fails to match the predicted fusion rules derived from the cyclic anomaly.

read the original abstract

We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a prescribed mixed anomaly, we show that gauging one factor produces a theory with a 2-group symmetry, while gauging the other yields a theory with a non-invertible 0-form symmetry, whose fusion rules we derive explicitly. When the parent theory possesses three such symmetries with a cyclic anomaly structure, gauging different factors can produce mutually dual theories and the half-spacetime gauging of the 2-group is implemented by a non-invertible duality defect, whose fusion rules we obtain. We illustrate the construction with explicit examples, including a $U(1)\times U(1)\times U(1)$ gauge theory and a general class of product theories. We also include a self-contained pedagogical introduction to the cohomological tools employed throughout the article.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

read the letter

This paper gives an explicit construction for non-invertible duality defects in 3d QFTs by half-spacetime gauging of 2-group symmetries that come from mixed anomalies between discrete Abelian 0-form symmetries, along with worked-out fusion rules and concrete examples. They start from a parent theory with two or three such symmetries carrying a prescribed mixed anomaly. Gauging one factor produces a 2-group symmetry while gauging the other produces a non-invertible 0-form symmetry. The half-spacetime gauging then turns the 2-group into a duality defect, and they derive the fusion rules in general before specializing to the cyclic anomaly case where different gaugings yield mutually dual theories. They illustrate everything with a U(1)^3 gauge theory and a class of product theories, and they include a self-contained section on the cohomological tools. What stands out is that the construction is concrete and the fusion algebra is stated explicitly rather than left at the level of abstract existence. The anomaly inflow and interface definitions line up without obvious contradictions, and the examples let you check the rules in practice. A softer spot is that the parent theories stay within Abelian discrete symmetries and specific anomaly structures, mostly gauge or free product models. It is not yet clear how far the method reaches into strongly coupled or non-Abelian settings without additional work. This paper is for people already working on generalized symmetries, 2-groups, and non-invertible defects in three-dimensional QFTs. A reader who knows the standard anomaly and gauging language will get direct value from the explicit rules and the examples. It deserves peer review because the claims are constructive, the derivations are laid out, and the checks on models are provided.

Referee Report

0 major / 2 minor

Summary. The manuscript constructs non-invertible duality defects in (2+1)d quantum field theories by performing half-spacetime gauging of 2-group symmetries. Starting from a parent theory with two (or three) discrete Abelian 0-form symmetries carrying a prescribed mixed anomaly, ordinary gauging of one factor yields a 2-group symmetry while gauging the other produces a non-invertible 0-form symmetry; when three symmetries with cyclic anomaly structure are present, the procedure generates mutually dual theories connected by a non-invertible duality defect. The fusion rules of these defects are derived explicitly, the construction is illustrated with concrete models including U(1)^3 gauge theory and product theories, and a self-contained pedagogical introduction to the relevant cohomological tools is provided.

Significance. If the central construction and explicit fusion-rule derivations hold, the work supplies a systematic, anomaly-driven mechanism for producing non-invertible duality defects in three-dimensional theories, extending the toolkit for generalized symmetries. The provision of concrete examples together with the self-contained cohomological background increases the accessibility and potential applicability of the results to further studies of duality and anomaly inflow in (2+1)d QFTs.

minor comments (2)

The abstract and introduction state that fusion rules are derived explicitly, yet a compact summary table or equation block collecting the final fusion algebra (including the non-invertible defect) would improve readability for readers primarily interested in the defect algebra.
In the U(1)^3 gauge-theory example, the text refers to the cyclic anomaly structure; an explicit listing of the three anomaly coefficients (or the corresponding 3-cocycle) in that section would allow immediate verification of the cyclic condition without cross-referencing the general setup.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript, including the accurate summary of our construction and the recommendation for minor revision. The referee's description correctly reflects the content and contributions of the work on non-invertible duality defects from half-spacetime gauging of 2-group symmetries.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs non-invertible duality defects via half-spacetime gauging starting from a parent theory with prescribed discrete Abelian 0-form symmetries and mixed anomalies. It performs standard gauging operations to produce 2-group or non-invertible symmetries, derives explicit fusion rules for the defects, and verifies on concrete models (U(1)^3 gauge theory and product theories). A self-contained pedagogical introduction to the cohomological classification tools is provided within the manuscript itself, avoiding reliance on external or self-cited results for the core steps. No equations reduce by construction to fitted inputs, no load-bearing self-citations justify uniqueness or ansatze, and no known results are merely renamed. The chain is independent and externally falsifiable via standard anomaly inflow and defect fusion algebra checks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard mathematical structures for symmetries and anomalies rather than new free parameters or invented entities.

axioms (1)

standard math Group cohomology classifies mixed anomalies between discrete Abelian 0-form symmetries and the structure of 2-group symmetries.
Invoked throughout the construction of the parent theories and the gauging procedures.

pith-pipeline@v0.9.0 · 5482 in / 1363 out tokens · 24239 ms · 2026-05-08T07:44:36.354531+00:00 · methodology

discussion (0)

Reference graph

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