Overlap Fermion in External Gravity

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.

Comments: 7 pages, talk presented at Lattice2006(Beyond QCD: Large N, Higgs, SUSY, Gravity, Strings)