Chiral fermion on curved domain-wall

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.