Non-Invertible Symmetry Webs

Bhardwaj, Lakshya; Bottini, Lea E.; Schäfer‐Nameki, Sakura; Tiwari, Apoorv

doi:10.48550/arxiv.2212.06842

Cited by 4 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[48][49][50][51][52][53][54] advocate their noninvertible symmetry nature. Only recently, noninvertible symmetries have been explored more systematically in higher spacetime dimensions, see selective references [55][56][57][58][59][60][61] relevant for the 4d SM or BSM context, see selective mathematically grandiose encyclopedic references [62][63][64][65][66][67], and references therein. Importantly Ref.…”

Section: Introduction Andmentioning

confidence: 99%

Categorical Symmetry of the Standard Model from Gravitational Anomaly

Putrov¹,

Wang²

2023

Preprint

View full text Add to dashboard Cite

In the Standard Model, some combination of the baryon B and lepton L number symmetry is free of mixed anomalies with strong and electroweak su(3) × su(2) × u(1) Ỹ gauge forces. However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent for leptogenesis in the very early universe. This happens when the "sterile right-handed" neutrino number nν R is not equal to the family number N f . Thus the invertible B − L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by Z and Z16 respectively. For this construction, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, or the 3d boundary topological order of 4d Z T F 4 -time-reversal symmetric topological superconductor.

show abstract

Section: Introduction Andmentioning

confidence: 99%

Categorical Symmetry of the Standard Model from Gravitational Anomaly

Putrov¹,

Wang²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…However, this fusion 2category is not Z/2-graded as the smallest normal subgroup of S 3 containing Z/2 is S 3 . This last fact is also reflected in the fusion rules (for instance, see [BBSNT22]). Nevertheless, we may view C(S 3 , Z/2, triv, triv) as an example of a near-group fusion 2-category.…”

Section: Examplesmentioning

confidence: 81%

“…We begin by introducing a categorification of the notion of a grouptheoretical fusion 1-category using work of the first author on fusion 2-categories [Déc23c,Déc23a]. Fusion 2-categories can be used to describe the interactions of topological operators (surfaces and lines) for (2 + 1)-dimensional theories and we note that group-theoretical fusion 2-categories have already appeared in the Physics literature [BBSNT23] (see also [BBFP22b,BBSNT22]). In particular, such fusion 2-categories are exactly the ones that arise by considering a finite group G, potentially equipped with an anomaly π, and gauging a subgroup H, equipped with a trivialization ψ of the anomaly.…”

Section: Resultsmentioning

confidence: 99%

“…We note that the Tambara-Yamagami 2-category 2TY(Z/2, triv) has first appeared in [BBSNT23], and then in [BBFP22a,BBFP22b,BBSNT22], which provided the original motivation for this work. Following [Tam00], it is interesting to try to determine when a Tambara-Yamagami 2-category admits a fiber 2-functor.…”

Section: Resultsmentioning

confidence: 99%

“…Group-theoretical fusion 1-categories were implicitly introduced in [Ost03b], and later explicitly in [ENO05]. We will study a strong categorification of this notion, which was first considered in the Physics literature [BBSNT23,BBFP22b,BBSNT22].…”

Section: Definition and Characterizationmentioning

confidence: 99%

See 2 more Smart Citations

The relative Deligne tensor product over pointed braided fusion categories

Décoppet

2023

Journal of Algebra

View full text Add to dashboard Cite

One-form symmetries in $\mathcal{N} = 3$ S-folds

Amariti,

Morgante,

Pasternak

et al. 2023

SciPost Phys.

View full text Add to dashboard Cite

We classify the global one-form symmetries for non-Lagrangian \mathcal{N}=3𝒩=3 SCFTs that arise by the action of SS-fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of (p, q)(p,q)-strings in the brane setup. The charge lattice of lines is then obtained by finding the ones that are genuine modulo screening by dynamical particles. The one-form symmetries are then extracted from the maximal sub-lattices of mutually local lines. We further comment on the existence of non-invertible symmetries for some of these \mathcal{N}=3𝒩=3 SCFTs.

show abstract

Non-Invertible Symmetry Webs

Cited by 4 publications

References 0 publications

Categorical Symmetry of the Standard Model from Gravitational Anomaly

Categorical Symmetry of the Standard Model from Gravitational Anomaly

The relative Deligne tensor product over pointed braided fusion categories

One-form symmetries in $\mathcal{N} = 3$ S-folds

Contact Info

Product

Resources

About