# The Chiral Dirac Determinant According to the Overlap Formalism

## TL;DR

This paper evaluates the chiral Dirac determinant using the overlap formalism, demonstrating its consistency with continuum results for gauge fields, thereby validating the formalism's effectiveness.

## Contribution

It provides the first detailed comparison showing the overlap formalism reproduces continuum chiral Dirac determinants for gauge backgrounds.

## Key findings

- Real and imaginary parts match continuum results
- Overlap formalism passes a key theoretical test
- Supports use of overlap formalism in chiral gauge theories

## Abstract

The chiral Dirac determinant is calculated using the overlap formalism of Narayanan and Neuberger. We compare the real and imaginary parts of the determinant with the continuum result for perturbative gauge field backgrounds and show that they are identical. Thus we find that the overlap formalism passes a crucial test.