Overlap Fermion in External Gravity

TL;DR

This paper develops a lattice formulation of overlap fermions in external gravitational fields, maintaining local Lorentz symmetry and aiming to recover general covariance in the continuum limit.

Contribution

It introduces a lattice overlap Dirac operator for fermions in external gravity, explicitly realizing local Lorentz symmetry as a gauge symmetry.

Findings

Lattice index density in gravitational fields calculated.

Framework for fermions in lattice gravity established.

Abstract

On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. The lattice index density in the presence of a gravitational field is calculated.