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

Abstract

The Dirac theory in the Euclidean Taub–NUT space gives rise to a large collection of conserved operators associated with 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.