Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space

TL;DR

This paper explores the algebraic structures arising from the Dirac theory in Euclidean Taub-NUT space, revealing an infinite-dimensional superalgebra related to hidden symmetries and monopole configurations.

Contribution

It introduces a specific infinite-dimensional superalgebra associated with the Dirac theory on manifolds with Gross-Perry-Sorkin monopoles, modeled as a twisted loop superalgebra.

Findings

Existence of an infinite-dimensional superalgebra in the Dirac theory

Identification of the superalgebra as a twisted loop superalgebra

Connection between symmetries and algebraic structures in monopole backgrounds

Abstract

The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even infinite-dimensional algebras or superalgebras. One presents here the infinite-dimensional superalgebra specific to the Dirac theory in manifolds carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an infinite-dimensional superalgebra that can be seen as a twisted loop superalgebra.