Killing-Yano equations and G-structures

Abstract

We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n),U(n),SU(n),Sp(n)\cdot Sp(1),Sp(n),G_2$ and $Spin(7)$. Solutions include nearly-Kähler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds. As an application, we find that particle probes on $Ad{S}_4\times X$ compactifications of type IIA and 11-dimensional supergravity admit a $\mathcal{W}$-type of symmetry generated by the fundamental forms. We also explore the $\mathcal{W}$-symmetries of string and particle actions in heterotic and common sector supersymmetric backgrounds. In the heterotic case, the generators of the $\mathcal{W}$-symmetries completely characterize the solutions of the gravitino Killing spinor equation, and the structure constants of the $\mathcal{W}$-symmetry algebra depend on the solution of the dilatino Killing spinor equation.

10 pages, minor changes

References in corpus (19)

• The Geometry of D=11 Killing Spinors
• SUSY in the sky
• HKT and OKT Geometries on Soliton Black Hole Moduli Spaces
• The intrinsic torsion of SU(3) and G_2 structures
• The Geometry of D=11 Null Killing Spinors
• Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
• The spinorial geometry of supersymmetric backgrounds
• The spinorial geometry of supersymmetric heterotic string backgrounds
• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• Geometry of all supersymmetric type I backgrounds
• Holonomy groups and W-symmetries
• Supersymmetric heterotic string backgrounds
• Killing-Yano Supersymmetry in String Theory
• Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
• Open G2 Strings
• On the symmetries of special holonomy sigma models
• Geometry of type II common sector N=2 backgrounds
• Wess-Zumino sigma models with non-Kahlerian geometry
• The intrinsic torsion of almost quaternion-Hermitian manifolds

Cited by in corpus (26)

• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Killing-Yano tensors and some applications
• Some remarks on (super)-conformal Killing-Yano tensors
• Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
• Geometry of Lax pairs: particle motion and Killing-Yano tensors
• New currents with Killing-Yano tensors
• Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
• Symmetry operators of Killing spinors and superalgebras in AdS_5
• A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
• Tensionless Strings and Killing(-Yano) Tensors
• Uses of Killing and Killing-Yano Tensors
• Killing-Yano Cotton Currents
• Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
• Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
• Hidden Symmetries and Integrability in Higher Dimensional Rotating Black Hole Spacetimes
• TCFHs, hidden symmetries and type II theories
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• TCFHs, hidden symmetries and M-theory backgrounds
• Higher-dimensional lifts of Killing-Yano forms with torsion
• The fundamental form of almost-quaternionic Hermitian manifolds
• TCFHs, IIB warped AdS backgrounds and hidden symmetries
• TCFHs and hidden symmetries of type IIA AdS backgrounds
• The TCFHs of D=11 AdS backgrounds and hidden symmetries
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
• Geometric Realizability of Covariant Derivative Kähler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds