Abstract
We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.
Highlights
Introduction and summarySymmetries of dynamical equations have always played very important role in string theory
Since the mKYT equation is written in the string frame, S duality induces a conformal rescaling of such metric, so generically the modified Killing-Yano tensor is destroyed by such operation
We have demonstrated that nontrivial Killing tensors in arbitrary number of dimensions are always associated with ellipsoidal coordinates, and we used this observation to construct the Killing(-Yano) tensors for the Myers-Perry black hole ((3.20), (3.30), (3.31)), its charged version (5.3)–(5.4), and for several examples of F1-NS5 geometries ((5.15), (5.19)–(5.21))
Summary
Symmetries of dynamical equations have always played very important role in string theory. Since at low energies strings behave as point particles, integrability must survive as a hidden symmetry of such objects, and this gives a very coarse necessary condition for integrability, which can be tested for large classes of backgrounds This condition was sufficient for ruling out integrability on all known supersymmetric geometries produced by D-branes, with an exception of AdSp×Sq and a couple of other examples [19]. Over the last four decades Killing(-Yano) tensors have been found for other geometries both in general relativity [40,41,42,43,44] and in string theory [45, 46], and in this article we will construct KYT for a large class geometries in arbitrary numbers of dimensions, which contains most of the known examples as special cases.
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