THE MOST GENERAL BPS BLACK HOLE FROM TYPE II STRING THEORY ON A SIX–TORUS: THE MACROSCOPIC–MICROSCOPIC CORRESPONDENCE

BPS black hole solutions in supergravity have been playing an important role in probing non–perturbative superstring dualities. The largest of these dualities is the conjectured U–duality, implemented by a discrete group of transformations U(Z), which represents the ultimate connection between all known superstring theories realized on various backgrounds. This picture suggests the existence of a unique fundamental quantum theory underlying the superstring theories, of which U–duality is an exact symmetry. In [1] this U–duality was conjectured to be encoded in the largest global symmetry group of the the field equations and Bianchi identities in the low–energy effective supergravity theory, which is described at classical level by a continuous semisimple Lie group U. The degree of supersymmetry preserved by BPS black holes in supergravity protects their physical quantities to a certain extent from quantum corrections so that they can be thought to correspond to solutions of superstring theory. Since moreover the BPS condition is U–duality invariant, these solutions naturally span an orbit of the U–duality group, which is a continuous collection of solutions at classical supergravity level and a discrete set at the superstring level. Supergravity represents the framework in which these orbits can be studied in most detail . A fruitful strategy therefore in order to study the microscopic features of BPS black holes in relation to their U–duality invariant properties would be to keep track in a precise mathematical fashion of the microscopic description of BPS black holes at this low–energy level and moreover to focus on the most general BPS black hole in a certain orbit modulo U–duality transformations, namely the generating solution. This is the main philosophy motivating the research project carried out in [3,4,5] where a macroscopic (supergravity) starting point was adopted for a systematic microscopic analysis of regular BPS (static, spherically symmetric) black holes within type II (M) theory compactified down to four dimensions on tori, and whose zero modes are described by N = 8 four dimensional supergravity. The U–duality group of this theory is U = E₇₍₇₎ [6]. This class of black holes was shown to preserve 1/8 of the original supersymmetries and to be characterized by five U–duality invariants (one of which being the entropy) …

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