Categorical Symmetry of the Standard Model from Gravitational Anomaly

Abstract

In the Standard Model, some combination of the baryon $\mathbf{B}$ and lepton $\mathbf{L}$ number symmetry is free of mixed anomalies with strong and electroweak $su(3)\times su(2)\times u(1{)}_{\tilde{Y}}$ gauge forces. However, it can still suffer from a mixed gravitational anomaly, hypothetically pertinent to leptogenesis in the very early universe. This happens when the total "sterile right-handed" neutrino number $n_{{\nu }_R}$ is not equal to the family number $N_f$. Thus the invertible $\mathbf{B}-\mathbf{L}$ symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical $\mathbf{B}-\mathbf{L}$ generalized 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 $\mathbb{Z}$ and ${\mathbb{Z}}_{16}$ respectively. For this construction, we utilize the anomaly inflow bulk-boundary correspondence, the 4d Pontryagin class and the gravitational Chern-Simons 3-form, the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate rational chiral central charge, and the 4d ${\mathbb{Z}}_4^{\mathrm{TF}}$-time-reversal symmetric topological superconductor with 3d boundary topological order.

34 pages. v2: refinements with new tables and appendices, including discussions on Atiyah's 2-framing and $p_1$ structures

References in corpus (21)

• Generalized Global Symmetries
• Leptogenesis
• Symmetries and Strings in Field Theory and Gravity
• Duality and defects in rational conformal field theory
• Generalized Symmetries in Condensed Matter
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Topological boundary conditions in abelian Chern-Simons theory
• Non-Invertible Higher-Categorical Symmetries
• Universal Non-Invertible Symmetries
• Unifying Constructions of Non-Invertible Symmetries
• Non-Invertible Symmetry Webs
• Non-invertible Symmetries and Higher Representation Theory I
• Line Operators in the Standard Model
• Non-invertible Symmetries and Higher Representation Theory II
• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• Estimating global charge violating amplitudes from wormholes
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Cobordism and Deformation Class of the Standard Model
• Ultra Unification
• Proton Stability: From the Standard Model to Beyond Grand Unification

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• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states
• Center Symmetry Breaking in Calabi--Yau Compactifications
• Anomaly of 4d Weyl fermions with discrete symmetries