HET-Discovery seminar by Hidenori Fukaya – University of Copenhagen

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HET-Discovery seminar by Hidenori Fukaya

Title: Six-dimensional regularization of chiral gauge theories on a lattice

Abstract: We propose a non-perturbative regularization of four dimensional chiral gauge theories.
In our formulation, we consider a Dirac fermion in six dimensions with two different mass terms having domain-wall profiles in the fifth- and the six-th 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 mediates 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 a massive vector-like theory, a non-perturbative regularization is 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.