Juven Wang - Open Problems in Physics and Novel Solutions from Math @ Harvard CMSA/12/08/2023

Juven Wang (Harvard)

Title:
Open Problems in Physics and Novel Solutions from Math


Abstract:
(1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis?

(2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions?

(3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry?

(4) Family/Generation problem: Why are there three families/generations of quarks and leptons?

In my talk, I will sketch and propose novel solutions to these challenging open problems in physics based on my own work (available on arXiv, some jointly with my collaborators).

I will show that the eclectic cross-disciplinary fertilization of ideas between the Math-Physics geometry and topology, Quantum Condensed Matter, and High-Energy Physics (theory, pheno, lattice) can help solving these big problems.

The (1) answer relates to Ultra Unification: a Z_{16} class Atiyah-Patodi-Singer eta invariant (Baryon - Lepton)-protected topological superconductor and a symmetry-extended anomalous topological quantum field theory.

The (2) and (3) answers relate to a trivial cobordism class and Symmetric Mass Generation, and disordering and removing the Pecci-Quinn axions.

The (4) answer has to do with the Hirzebruch signature and Atiyah-Singer index theorem, gravitational Chern-Simons theory, and 3 E8 quantum Hall states.

References:
https://arxiv.org/abs/2012.15860
https://doi.org/10.1103/PhysRevD.103....

https://arxiv.org/abs/1809.11171
https://doi.org/10.1103/PhysRevResear...

https://arxiv.org/abs/2207.14813
https://doi.org/10.1103/PhysRevD.106....

https://arxiv.org/abs/2204.14271
https://doi.org/10.3390/sym14071475

https://arxiv.org/abs/2312.14928
https://arxiv.org/abs/2312.17126

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