Topological Field Theory of Vortices over Closed Kahler Manifolds

TL;DR

This paper develops a topological field theory for vortices on closed Kahler manifolds by dimensional reduction of Einstein-Hermitian equations, introducing a Yang-Mills-Higgs functional with topological invariance and ghost fields.

Contribution

It introduces a novel higher-dimensional topological field theory for vortices, derived from Einstein-Hermitian equations via dimensional reduction, incorporating ghost fields for topological invariance.

Findings

Dimensional reduction links Einstein-Hermitian equations to vortex equations.

A Yang-Mills-Higgs functional with topological invariance is constructed.

Matter-coupled topological field theories are achieved in higher dimensions.

Abstract

By dimensional reduction, Einstein-Hermitian equations of n + 1 dimensional closed Kahler manifolds lead to vortex equations of n dimensional closed Kahler manifolds. A Yang-Mills-Higgs functional to unitary bundles over closed Kahler manifolds has topological invariance by adding the additional terms which have ghost fields. Henceforth we achieve the matter (Higgs field) coupled topological field theories in higher dimension.