Chiral fermion on curved domain-wall

TL;DR

This paper investigates how chiral fermions on curved domain-walls embedded in a lattice can reveal gravitational effects through their spectral properties, extending flat domain-wall fermion models to curved geometries.

Contribution

It introduces a lattice model of fermions on curved domain-walls and demonstrates how gravitational effects are reflected in the Dirac spectrum for $S^1$ and $S^2$ geometries.

Findings

Chiral massless modes appear at the curved domain-wall.

Gravity effects are detectable via the Dirac operator spectrum.

The model extends flat domain-wall fermions to curved geometries.

Abstract

We consider a massive fermion system having a curved domain-wall embedded in a square lattice. In a similar way to the conventional flat domain-wall fermion, chiral massless modes appear at the domain-wall but these modes feel "gravity" through the induced spin connections. In this work, we embed $S^1$ and $S^2$ domain-walls into a Euclidean space and show how the gravity is detected from the spectrum of the Dirac operator.