Six-dimensional regularization of chiral gauge theories on a lattice
arXiv:1612.00096
Abstract
We propose a six-dimensional regularization of four dimensional chiral gauge theories. We consider a massive Dirac fermion in six dimensions with two different operators having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of the two domain-walls. In our formulation, the Stora-Zumino chain of the anomaly descent equations, starting from the axial anomaly in six-dimensions to the gauge anomaly in four-dimensions, is naturally embedded. Moreover, a similar inflow of the global anomalies is found. The anomaly free condition is equivalent to requiring that the axial anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. 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.
14pages, 2figures, Proceedings of the 34th annual International Symposium on Lattice Field Theory. PoS(LATTICE2016)330, References added