Integrability of the Dirac Equation in the Presence of Fluxes on Product Manifolds

TL;DR

This paper demonstrates that the Dirac equation with fluxes can be separated on product manifolds, and applies this to analyze a spin-1/2 particle in a complex string-inspired 10D background with fluxes.

Contribution

It establishes the separability of the Dirac equation with fluxes on product manifolds and applies it to a novel 10-dimensional string-inspired model.

Findings

Separation of the Dirac equation in flux backgrounds on product manifolds

Application to a 10D string-inspired model with fluxes

Analysis of spin-1/2 particle propagation in complex flux backgrounds

Abstract

This paper aims to show that the Dirac equation coupled to an arbitrary inhomogeneous flux field admits separation in manifolds formed from the direct product of bidimensional spaces. As a direct application of these results, we study a spin-$1/2$ charged particle propagating in a background conformally related to a novel and complex string-inspired model in $D = 10$ spacetime dimension whose base manifold is a product of four two-dimensional unit spheres, $S^{2}$, in the presence of $1$- and $3$-form fluxes.