8 research outputs found
Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups
We study the minimal unitary representations of noncompact exceptional groups
that arise as U-duality groups in extended supergravity theories. First we give
the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well
as SU(6,2) covariant bases. E_{8(-24)} has E_7 X SU(2) as its maximal compact
subgroup and is the U-duality group of the exceptional supergravity theory in
d=3. For the corresponding U-duality group E_{8(8)} of the maximal supergravity
theory the minimal realization was given in hep-th/0109005. The minimal unitary
realizations of all the lower rank noncompact exceptional groups can be
obtained by truncation of those of E_{8(-24)} and E_{8(8)}. By further
truncation one can obtain the minimal unitary realizations of all the groups of
the "Magic Triangle". We give explicitly the minimal unitary realizations of
the exceptional subgroups of E_{8(-24)} as well as other physically interesting
subgroups. These minimal unitary realizations correspond, in general, to the
quantization of their geometric actions as quasi-conformal groups as defined in
hep-th/0008063.Comment: 28 pages. Latex commands removed from the abstract for the arXiv. No
changes in the manuscrip
Jordan Pairs, E6 and U-Duality in Five Dimensions
By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3
and the relation to the super-Ehlers symmetry in D = 5, we elucidate the
massless multiplet structure of the spectrum of a broad class of D = 5
supergravity theories. Both simple and semi-simple, Euclidean rank-3 Jordan
algebras are considered. Theories sharing the same bosonic sector but with
different supersymmetrizations are also analyzed.Comment: 1+41 pages, 1 Table; v2 : a Ref. and some comments adde
Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
In these lecture notes, we review some recent developments on the relation
between the macroscopic entropy of four-dimensional BPS black holes and the
microscopic counting of states, beyond the thermodynamical, large charge limit.
After a brief overview of charged black holes in supergravity and string
theory, we give an extensive introduction to special and very special geometry,
attractor flows and topological string theory, including holomorphic anomalies.
We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates
microscopic degeneracies to the topological string amplitude, and review
precision tests of this formula on ``small'' black holes. Finally, motivated by
a holographic interpretation of the OSV conjecture, we give a systematic
approach to the radial quantization of BPS black holes (i.e. quantum
attractors). This suggests the existence of a one-parameter generalization of
the topological string amplitude, and provides a general framework for
constructing automorphic partition functions for black hole degeneracies in
theories with sufficient degree of symmetry.Comment: 103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important
upgrade, prepared for the proceedings of Frascati School on Attractor
Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more
figures, more refs, and minor changes in abstract and introductio