Gravitational Lorentz anomaly from the overlap formula in 2-dimensions

TL;DR

This paper demonstrates that the overlap formulation of chiral gauge theories accurately reproduces the gravitational Lorentz anomaly in two dimensions, linking lattice methods with gravitational anomaly calculations.

Contribution

It shows that the overlap formulation correctly captures the gravitational Lorentz anomaly in 2D, connecting lattice fermion approaches with gravitational anomaly responses.

Findings

Overlap formulation reproduces gravitational Lorentz anomaly in 2D

Effective action response to coordinate transformations is recovered

Supports overlap approach as a solution to fermion doubling on the lattice

Abstract

In this letter we show that the overlap formulation of chiral gauge theories correctly reproduces the gravitational Lorentz anomaly in 2-dimensions. This formulation has been recently suggested as a solution to the fermion doubling problem on the lattice. The well known response to general coordinate transformations of the effective action of Weyl fermions coupled to gravity in 2-dimensions can also be recovered.