Half-Spacetime Gauging of 2-Group Symmetry in 3d
Davide Bason, Wei Cui, Lorenzo Ruggeri
TLDR
This paper constructs non-invertible duality defects in 3d quantum field theories by half-spacetime gauging of 2-group symmetry.
Key contributions
- Constructs non-invertible duality defects in 3d QFTs via half-spacetime gauging of 2-group symmetry.
- Explores how gauging 0-form symmetries in parent theories yields 2-group or non-invertible symmetries.
- Explicitly derives fusion rules for the resulting non-invertible 0-form and duality defects.
- Provides concrete examples, such as U(1)xU(1)xU(1) gauge theory, to illustrate the construction.
Why it matters
This work advances our understanding of non-invertible symmetries and duality defects in 3d QFTs. It offers a systematic construction method and explicit examples, providing crucial tools for theoretical physics research.
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.
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