Abstract
We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain-walls. One domain-wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six-dimensions to the gauge anomaly in four-dimensions. Another domain-wall implies a similar inflow of the global anomalies. The anomaly free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is based on a massive vector-like fermion determinant, a non-perturbative regularization will be possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.
Highlights
Defining chiral fermions on a lattice has been a big challenge since Nielsen and Ninomiya [1, 2] proved the no-go theorem about chiral symmetry without unphysical doublers
We have proposed a 6-dimensional regularization of the chiral gauge theories in 4dimensions
When M1 and M2 both commute with D 5D, this determinant is real but positive
Summary
Defining chiral fermions on a lattice has been a big challenge since Nielsen and Ninomiya [1, 2] proved the no-go theorem about chiral symmetry without unphysical doublers. It was shown that the global anomaly can be formulated as the complex phase of the bulk 5-dimensional theory, which has 4-dimensional target (massless) fermions on its boundary. The extra dimension for the global anomaly is introduced as a one-parameter family of the fermion determinant phase where the chiral fermions are already put on a 4-dimensional space. [24, 25], it was shown that the phase of the Weyl fermion determinant can be given by the η-invariant of a Dirac operator extended in 5 dimensions This η-invariant needs a variation with respect to another oneparameter family We formulate a vector-like 6-dimensional Dirac fermion system in which Weyl fermions are localized at the junction of two different kinds of domain walls. In the following analysis, we use the simple axial vector current background operator
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