Ultra Unification & Noninvertible Symmetry of Standard Model via Gravitational Anomaly @ NYU AD GTP

Juven Wang (Harvard University CMSA) @ NYU Abu Dhabi GTP 11/01/2023

Geometry, Topology, and Physics (GTP) Seminar series at the Center for Quantum and Topological Systems @ New York University Abu Dhabi


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Title: Ultra Unification, and Noninvertible Symmetry of the Standard Model from Gravitational Anomaly

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Abstract: In the Standard Model, the total "sterile right-handed" neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in the previous work on Cobordism and Deformation Class of the Standard Model [arxiv:2112.14765, arxiv:2204.08393] and Ultra Unification [arxiv:2012.15860], in order to predict new highly entangled sectors beyond the Standard Model. Ultra Unification would combine the Standard Model and Grand Unification, particularly for the models with 15 Weyl fermions per family, without the necessity of right-handed sterile neutrinos, by adding new gapped topological phase sectors (in 4d or 5d) or new gapless interacting conformal sectors (in 4d) consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the mixed gauge-gravitational anomaly, such as a ℤ_{16} class anomaly, associated with the baryon minus lepton number B−L and the electroweak hypercharge Y).

Moreover, for the Standard Mode alone, the invertible B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons, hypothetically pertinent for leptogenesis in the very early universe. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we construct 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 ℤ_{16} respectively. For this construction, we utilize the anomaly inflow concept, the 4d Pontryagin class and the gravitational Chern-Simons 3-form, the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory with a framing anomaly corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, and the 4d Z_4^{TF}-time-reversal symmetric topological superconductor with 3d boundary topological order [arxiv:2302.14862].