A lattice regularization of Weyl fermions in a gravitational background

Author:

Shoto Aoki, Hidenori Fukaya, Naoto Kan

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Strongly Correlated Electrons (cond-mat.str-el), High Energy Physics - Theory (hep-th)

journal:

OU-HET-1214

date:

2024-01-11 00:00:00

Abstract

We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, we showed under the time-reversal symmetry that the edge-localized massless Dirac fermion appears on one and two-dimensional spherical domain-walls and the spin connection is induced on the lattice in a consistent way with continuum theory. In this work, we extend our study to the Shamir type curved domain-wall fermions without the time-reversal symmetry. We find in the free fermion case that a single Weyl fermion appears on the edge, and feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero mode at the center where the gauge field is singular.

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