Supersymmetric probes on the conifold

We study the supersymmetric embeddings of different D-brane probes in the AdS_5 x T^{1,1} geometry. The main tool employed is kappa symmetry and the cases studied include D3-, D5- and D7-branes. We find a family of three-cycles of the T^{1,1} space over which a D3-brane can be wrapped supersymmetrically and we determine the field content of the corresponding gauge theory duals. Supersymmetric configurations of D5-branes wrapping a two-cycle and of spacetime filling D7-branes are also found. The configurations in which the entire T^{1,1} space is wrapped by a D5-brane (baryon vertex) and a D7-brane are also studied. Some other embeddings which break supersymmetry but are nevertheless stable are also determined.Comment: 44 pages, LaTeX; v2: typos corrected, references added, discussion of D5-brane embeddings improve

Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables

In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing-Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can "generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing-Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general Kerr-NUT-(A)dS metrics.Comment: 33 pages, no figures, updated references and corrected typo

Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims