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.
Highlights
Quite recently [1, 2], Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator
We study the formulation in Refs. [1, 2] from the perspective of the fermion number anomaly [19, 20] and possible associated phenomenology
Assuming the validity of the formulation, especially the restoration of the locality for anomaly-free chiral gauge theories, we accept the existence of the fluff fermions positively and discuss possible phenomenological implications
Summary
Quite recently [1, 2], Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. They obtained this 4-dimensional formulation by taking the infinite 5th-dimensional extent limit in their 5dimensional domain-wall formulation in Ref. Assuming the validity of the formulation, especially the restoration of the locality for anomaly-free chiral gauge theories, we accept the existence of the fluff fermions positively and discuss possible phenomenological implications. Considering the transformation (2.16) with the localized parameter θ → θ(x), we have the anomalous conservation law of the fermion number current of the left-handed fermion,. The fermion number current of the right-handed fermion does not conserve:
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