Abstract
Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the original gauge field A, while the right-handed one is coupled only to the gauge field A*, a deformation of A by the gradient flow with infinite flow time. In this paper, we study the fermion one-loop effective action in their formulation. We show that the continuum limit of this effective action contains local interaction terms between A and A*, even if the anomaly cancellation condition is met. These non-vanishing terms would lead an undesired perturbative spectrum in the formulation.
Highlights
Introduction and discussionRecently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories [1]
This formulation is based on the so-called overlap operator, which can be obtained from their five-dimensional domain-wall formulation [2]1 by the traditional way [4,5,6]. In this formulation, along the fifth dimension, the original gauge field A is deformed by the gradient flow [7,8,9,10] for infinite flow time
The perturbative spectrum is modified in a weird way; this would not be what we want to obtain for chiral gauge theories. Since these effects in the one-loop effective action (16) should be removed by local counterterms, the formulation of Grabowska and Kaplan will be undesirable as a non-perturbative formulation of chiral gauge theories
Summary
Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories [1] This formulation is based on the so-called overlap operator, which can be obtained from their five-dimensional domain-wall formulation [2]1 by the traditional way [4,5,6]. The perturbative spectrum is modified in a weird way; this would not be what we want to obtain for chiral gauge theories Since these effects in the one-loop effective action (16) should be removed by local counterterms, the formulation of Grabowska and Kaplan will be undesirable as a non-perturbative formulation of chiral gauge theories. Their formulation with the abrupt transition should be improved in some possible way
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