Gauge Field Strength Tensor from the Overlap Dirac Operator

TL;DR

This paper demonstrates that the classical continuum limit of a specific trace involving the overlap Dirac operator accurately reproduces the gauge field strength tensor, bridging lattice and continuum gauge theories.

Contribution

It provides a derivation showing that the overlap Dirac operator's trace converges to the gauge field strength tensor in the continuum limit.

Findings

The trace of the overlap Dirac operator yields the gauge field strength tensor in the continuum limit.

The result establishes a direct link between lattice Dirac operators and continuum gauge fields.

Abstract

We derive the classical continuum limit of the operator tr$_s \sigma_{\mu\nu} D^{ov}(x,x)$ with $D^{ov}$ being the overlap Dirac operator and show that it corresponds to the gauge field strength tensor $F_{\mu\nu}(x)$.