Vortex solutions in the noncommutative torus

TL;DR

This paper explores vortex solutions in a noncommutative two-dimensional torus, extending numerical methods to analyze BPS equations in noncommutative Abelian Higgs models.

Contribution

It introduces a numerical approach for solving BPS equations on noncommutative tori, adapting algorithms from commutative space and utilizing the Fock space framework.

Findings

Constructed numerical solutions for self-dual and anti-self-dual vortices.

Extended existing algorithms to noncommutative geometries.

Demonstrated the use of Fock space and Moyal-Weyl methods for solution expression.

Abstract

Vortex configurations in the two-dimensional torus are considered in noncommutative space. We analyze the BPS equations of the Abelian Higgs model. Numerical solutions are constructed for the self-dual and anti-self dual cases by extending an algorithm originally developed for ordinary commutative space. We work within the Fock space approach to noncommutative theories and the Moyal-Weyl connection is used in the final stage to express the solutions in configuration space.