Lorentz symmetry violation in the fermion number anomaly with the chiral overlap operator

Abstract

Recently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories on the basis of a chiral overlap operator. We compute the classical continuum limit of the fermion number anomaly in this formulation. Unexpectedly, we find that the continuum limit contains a term which is not Lorentz invariant. The term is, however, proportional to the gauge anomaly coefficient, and thus the fermion number anomaly in this lattice formulation automatically restores the Lorentz-invariant form when and only when the anomaly cancellation condition is met.

arXiv comment9 pages, 2 figures

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• 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