Categorical Symmetry of the Standard Model from Gravitational Anomaly

In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This point of view allows us to treat symmetries and anomalous symmetries as non-invertible gravitational anomalies (which are also described by multi-component partition functions, transforming covariantly under the mapping group transformation...

Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturally arises near a gapless quantum critical region between Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4) \times su(2) \times su(2)$ models of quantum vacua (in a phase diagram or moduli space), by implementing a modified $so(10)$ Grand Unification (GUT) with a Spin(10) gauge group plus a new discrete Wess-Zumino Witten term matching a 4d nonperturbative global mixed gauge-gravity $w_2 w_3$ anomaly....

New phenomenological models of Quantum Gravity have suggested that a Lorentz-Invariant discrete spacetime structure may become manifest through a nonstandard coupling of matter fields and spacetime curvature. On the other hand, there is strong experimental evidence suggesting that neutrino oscillations cannot be described by simply considering neutrinos as massive particles. In this manuscript we motivate and construct one particular phenomenological model of Quantum Gravity ...

We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called "gauging" and "c...

In this thesis we study some theoretical and phenomenological aspects of classical conformal symmetry in specific extensions of the SM. We consider both supersymmetric and non supersymmetric cases. We discuss the perturbative structure of the superconformal anomaly effective action. We show that the manifestation of the anomaly is in the presence of massless intermediate states in correlators involving the Ferrara-Zumino supercurrent with two vector supercurrents. This univer...

Gravitational leptogenesis refers to a class of baryogenesis models in which the matter-antimatter asymmetry of the universe arises through the standard model lepton-number gravitational anomaly. In these models chiral gravitational waves source a lepton asymmetry in standard model neutrinos during the inflationary epoch. We point out that gravitational leptogenesis can be successful in either the Dirac or Majorana neutrino mass scenario. In the Dirac mass scenario, gravitati...

We introduce a new effect in the neutrino oscillation phase which shows the neutrino-antineutrino oscillation is possible under gravity even if the rest masses of the corresponding eigenstates are same. This is due to CPT violation and possible to demonstrate if the neutrino mass eigenstates are expressed as a combination of neutrino and antineutrino eigenstates, as of the neutral kaon system, with the plausible breaking of lepton number conservation. For Majorana neutrinos, ...

We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague $d=4$ $Sp(k)$ theories, is well-understood in terms of $\pi_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\pi_3(G)=\mathbb{Z}$, via the fermion zero mode counting. We revisit this relation and point out how $SU(N)$ theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly ca...

In the Standard Model at high temperatures, anomalous effects contribute to the violation of baryon number ($B$) and lepton number ($L$), separately, while $B-L$ remains conserved. There are also corresponding changes in the helicity of the hypermagnetic field ($h$) and the Chern-Simons numbers of the non-Abelian gauge fields ($N_{\rm CS,W}$ and $N_{\rm CS,S}$). In this study, we investigate a baryogenesis process in the symmetric phase of the early Universe by taking into ac...

In this work, we classify all the effective $U(1)$ symmetries and their associated Noether charges in the Standard Model (SM) and its minimal supersymmetric extension (MSSM) from the highest scale after inflation down to the weak scale. We then demonstrate that the discovery of the violation of baryon minus lepton number ($B-L$) which pinpoints to its violation in primordial Universe at any cosmic temperature above $30$ TeV will open up a new window of baryogenesis in these e...