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David Morrison : Non-Spherical Horizons

The ``horizon'' of N coincident branes in Minkowski space is the unit sphere in the transverse directions; in a certain scaling limit, string or M-theory in the presence of branes is dual to a compactification on the product of an anti-de Sitter space with the horizon. We study the analogous limit when N branes are placed at a singular point, so that the horizon becomes the so-called ``link'' of the singularity, and is no longer a sphere. A similar scaling argument leads to a natural extension of Maldacena's celebrated ``AdS/CFT correspondence conjecture'' to this situation. The conformal field theories in question have less supersymmetry than the cases studied by Maldacena, with the amount being determined by the Killing spinors on the horizon manifold. An important mathematical tool is the relationship -- derived some years ago by C. Bär -- between Killing spinors on a manifold and covariantly constant spinors on the cone over that manifold.

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