Continuum and Lattice Overlap for Chiral Fermions on the Torus

TL;DR

This paper demonstrates that the overlap formulation accurately computes the chiral determinant on a torus, with lattice results converging to continuum results as lattice spacing approaches zero, confirming the method's validity for chiral fermions.

Contribution

It shows that the lattice overlap reproduces continuum results for chiral determinants on a torus, validating its use in lattice gauge theory.

Findings

Continuum overlap yields correct string theory results.

Lattice overlap converges to continuum results as lattice spacing decreases.

Subleading lattice terms are irrelevant in the continuum limit.

Abstract

The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We evaluate first the continuum overlap, which is convergent and well-defined, and yields the correct string theory result for both the real and imaginary parts of the effective action. We then show that the lattice version of the overlap gives the continuum overlap results in the limit when the lattice spacing tends to zero, and that the subleading terms in that limit are irrelevant.