BPS Black Holes and U-duality

[kneemo]

Greetings Everyone!


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:

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.

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.


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