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 (1)

• Supersymmetric heterotic string backgrounds