  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.
