Fermion number anomaly with the fluffy mirror fermion

Abstract

Quite recently, Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. We study this formulation from the perspective of the fermion number anomaly and possible associated phenomenology. A simple argument shows that the consistency of the formulation implies that the fermion with the opposite chirality to the physical one, the "fluffy mirror fermion" or "fluff", suffers from the fermion number anomaly in the same magnitude (with the opposite sign) as the physical fermion. This immediately shows that if at least one of the fluff quarks is massless, the formulation provides a simple viable solution to the strong CP problem. Also, if the fluff interacts with gravity essentially in the same way as the physical fermion, the formulation can realize the asymmetric dark matter scenario.

10 pages, the final version to appear in PTEP

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Cited by in corpus (7)

• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Axial U(1) current in Grabowska and Kaplan's formulation
• One-loop perturbative coupling of $A$ and $A_{\star }$ through the chiral overlap operator
• On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories
• A calculation of the gauge anomaly with the chiral overlap operator