Symmetries of the Dirac operator with skew-symmetric torsion
arXiv:1002.3616 · doi:10.1088/0264-9381/27/18/185019
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.
arXiv comment19 pages, no figures
References in corpus (17)
- Rotating Charged Black Hole Solution in Heterotic String Theory
- Twistor spaces for HKT manifolds
- Geometry of Hyper-Kähler Connections with Torsion
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
- Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
- Dirac symmetry operators from conformal Killing-Yano tensors
- Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
- Generalized Killing-Yano equations in D=5 gauged supergravity
- Generalized hidden symmetries and the Kerr-Sen black hole
- Twistor Spaces for QKT Manifolds
- Killing tensors and a new geometric duality
- Symmetries of supergravity black holes
- Killing-Yano Supersymmetry in String Theory
- HKT Geometry and de Sitter Supergravity
- First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition
- Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory
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- Hidden Symmetry and Exact Solutions in Einstein Gravity
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- Killing-Yano equations with torsion, worldline actions and G-structures
- Local metrics admitting a principal Killing-Yano tensor with torsion
- Principal Tensor Strikes Again: Separability of Vector Equations with Torsion
- General Wahlquist Metrics in All Dimensions
- Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
- A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
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- Electron in higher-dimensional weakly charged rotating black hole spacetimes
- Hidden Symmetries and Integrability in Higher Dimensional Rotating Black Hole Spacetimes
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- Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
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- Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
- Hidden symmetries of black holes in five-dimensional supergravity
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