Categorical symmetry of the standard model from gravitational anomaly

Putrov, Pavel; Wang, Juven

doi:10.1103/PhysRevD.110.125028

Categorical symmetry of the standard model from gravitational anomaly

Pavel Putrov
(
- ICTP, Trieste
)
,
Juven Wang
(
- Harvard U., CMSA
)

Feb 28, 2023

34 pages

Published in:

Phys.Rev.D 110 (2024) 12, 125028

Published: Dec 15, 2024

e-Print:

2302.14862 [hep-th]

DOI:

10.1103/PhysRevD.110.125028 (publication)

View in:

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Abstract: (APS)

In the Standard Model, some combination of the baryon

B

and lepton

L

number symmetry is free of mixed anomalies with strong and electroweak

s u (3) \times s u (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_{ν_{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. Specifically, we show that a noninvertible categorical

B - 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

Z

and

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 with a framing anomaly corresponding to a 2D rational conformal field theory with an appropriate rational chiral central charge, and the 4D

Z_{4}^{TF}

-time-reversal symmetric topological superconductor with 3D boundary topological order.

Note:

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

anomaly: gravitation
gravitation: background
defect: topological
field theory: conformal: rational
phase: topological
charge: symmetry
charge: operator
superconductivity: topological
gravitation: instanton
current: conservation law

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