Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry
Abstract
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N=4 supersymmetry.
Cite
@article{arxiv.hep-th/0202034,
title = {Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry},
author = {Ion I. Cotăescu and Mihai Visinescu},
journal= {arXiv preprint arXiv:hep-th/0202034},
year = {2015}
}
Comments
14 pages, latex, no figures