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An interesting line of research that has recently surfaced in the stringy/sugra community is the counting of microstates of spherically symmetric BPS black holes in four-dimensional N ≥ 2 supergravity theories. The excitement stems from the indication that the U-duality groups (e.g. E6(6)(Z), E7(7)(Z), E8(8)(Z)) of certain "very special supergravities" may be spectrum generating symmetries for BPS black holes.

Here's a quote from the Dec 22 paper http://www.arxiv.org/abs/hep-th/0512296" [Broken] by Murat Gunaydin, Andrew Neitzke, et al:

Essentially the symmetric spaces receiving attention are those spaces generated by projective elements of exceptional Jordan algebras. One recovers the U-duality groups from the isometry, collineation, conformal, and quasiconformal groups of these spaces. Since the Jordan algebras are defined over the octonions and split-octonions, such symmetric spaces are inherently self-dual matrix spaces. I have discussed such matrix spaces with selfAdjoint on many occasions, and I am delighted the physics is now related to extremal black holes. The analysis we describe applies to a class of d = 4,

N = 2 supergravity theories whose scalar fields are associated

to vector multiplets and lie on a symmetric

space M4 = G4/K4. Such theories, known as “very special

supergravities”, were first studied in [26, 27, 28].

The special geometry of M4 turns out to be characterized

by a cubic prepotential F = N(X)/X0, with N(X) the

norm function of a degree 3 Jordan algebra J. The classification

and study of such theories is therefore closely

tied to the theory of Jordan algebras.

It is not yet clear if such results have a "stringy interpretation", but the implications are nonetheless exciting. For further background, read M. Gunaydin's http://www.arxiv.org/abs/hep-th/0506010" [Broken] and view/listen to the lectures given at the KITP site "[URL [Broken] Structures in String Theory (Aug 1 - Dec 16, 2005)

[/URL] by http://online.itp.ucsb.edu/online/strings05/pioline/" [Broken].

~M

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# BPS Black Holes and U-duality

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