CMSA Quantum Matter in Mathematics and Physics: Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem

In this talk, I will discuss a new solution to the strong CP problem, one of the most important and challenging problems, of the Standard Model (SM) based on the generalized global symmetry. To this end, I will first show that there exist non-invertible chiral symmetries acting on quark fields once the SM is extended with gauged quark flavor symmetry. Interestingly enough, such symmetries, which we named them as "non-invertible Peccei-Quinn symmetries", exist only because the SM has the same number of generations as colors, yet another feature that deserves a fundamental explanation. Then I discuss how these new generalized symmetries set the down Yukawa to be exactly zero and lead to a massless quark solution to the strong CP problem. Completion of the solution requires (i) generation of down quark Yukawas to be consistent with both observed quark mass spectrum and mixings and (ii) generation of O(1) CP violating phase called CKM phase, crucially without destabilizing our solution to the strong CP problem. I will discuss that these rather non-trivial tasks can be achieved by a UV completion in an SU(9) quark color-flavor unification.

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