Continuous generalized symmetries in three dimensions

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with GG 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [SciPost Phys. 15, 122 (2023)]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups GG, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.

Section: Maximal Symmetry Categories For Orthogonal Gauge Theoriesmentioning

confidence: 85%

Non-invertible symmetry webs

Bhardwaj,

Bottini,

Schäfer-Nameki

et al. 2023

“…In this case, non-invertible topological defects are potentially important, as well as junctions of domain walls. See [70,[107][108][109][110][111][112][113][114][115][116] for related work in various dimensions.…”

Section: Domain Wallsmentioning

confidence: 99%

Anomalies and symmetry fractionalization

Delmastro,

Gomis,

Hsin

et al. 2023

We study ordinary, zero-form symmetry GG and its anomalies in a system with a one-form symmetry \GammaΓ. In a theory with one-form symmetry, the action of GG on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of GG if the theory has an anomaly involving \GammaΓ. Therefore, the computation of the ’t Hooft anomaly for an ordinary symmetry GG generally requires first discovering the one-form symmetry \GammaΓ of the physical system. We show that the multiple values of the anomaly for GG can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in 2+1d2+1d gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial \mathbb{Z}_{2N}ℤ2N symmetry in 3+1d3+1d{\cal N}=1 super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in 2+1d2+1d\mathbb{Z}_2ℤ2 gauge theory.

“…where Vec is the 1-category of finite-dimensional vector spaces. 20 Such monoidal functors form the category Rep(Γ (0) ) of finite-dimensional representations of Γ (0) .…”

Section: Higher-categories Of Universalmentioning

confidence: 99%

Unifying constructions of non-invertible symmetries

Bhardwaj,

Schäfer-Nameki,

Tiwari

2023

In the past year several constructions of non-invertible symmetries in Quantum Field Theory in d≥3d≥3 have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta defects, which generalize the notion of theta-angles, and allow the construction of universal and non-universal topological symmetry defects. We complement this physical analysis by proposing a mathematical framework (based on higher-fusion categories) that converts the physical construction of non-invertible symmetries into a concrete computational scheme.