1. Symmetries of the Dirac operator with skew-symmetric torsion
- Author
-
C. M. Warnick, David Kubiznak, Yukinori Yasui, Tsuyoshi Houri, Warnick, Claude [0000-0001-7132-8319], and Apollo - University of Cambridge Repository
- Subjects
High Energy Physics - Theory ,Mathematics - Differential Geometry ,Physics and Astronomy (miscellaneous) ,FOS: Physical sciences ,Conformal map ,YANO TENSORS ,General Relativity and Quantum Cosmology (gr-qc) ,Dirac operator ,General Relativity and Quantum Cosmology ,symbols.namesake ,STRING THEORY ,KAHLER-MANIFOLDS ,EQUATION ,FOS: Mathematics ,Skew-symmetric matrix ,CONNECTIONS ,01 Mathematical Sciences ,Mathematical physics ,Physics ,02 Physical Sciences ,GEOMETRY ,Torsion (mechanics) ,Nuclear & Particles Physics ,Massless particle ,High Energy Physics - Theory (hep-th) ,Differential Geometry (math.DG) ,Dirac equation ,Homogeneous space ,CURVED SPACETIME ,symbols ,Mathematics::Differential Geometry - Abstract
In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion. We find that the generalized conformal Killing-Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise to symmetries of the Dirac operator in the case of strong Kahler with torsion (KT) and strong hyper-Kahler with torsion (HKT) manifolds., 19 pages, no figures
- Published
- 2010