Dirac Equation in the Background of the Nutku Helicoid Metric

TL;DR

This paper investigates solutions to the Dirac equation within the Nutku helicoid metric background, addressing the challenges posed by curvature singularities through spectral boundary conditions in both four and five dimensions.

Contribution

It introduces the application of Atiyah-Patodi-Singer spectral boundary conditions to the Dirac equation in Nutku helicoid metrics, including higher-dimensional cases.

Findings

Successfully formulated boundary conditions for singular metrics

Extended analysis to five-dimensional manifolds

Provided insights into fermionic behavior in complex geometries

Abstract

We study the solutions of the Dirac equation in the background of the Nutku helicoid metric. This metric has curvature singularities, which necessitates imposing a boundary to exclude this point. We use the Atiyah-Patodi-Singer non local spectral boundary conditions for both the four and the five dimensional manifolds.