254 research outputs found
N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
We analyze the Hessian matrix of the black hole potential of N=8, d=4
supergravity, and determine its rank at non-BPS critical points, relating the
resulting spectrum to non-BPS solutions (with non-vanishing central charge) of
N=2, d=4 magic supergravities and their ``mirror'' duals. We find agreement
with the known degeneracy splitting of N=2 non-BPS spectrum of generic special
Kahler geometries with cubic holomorphic prepotential. We also relate non-BPS
critical points with vanishing central charge in N=2 magic supergravities to a
particular reduction of the N=8, 1/8-BPS critical points.Comment: 1+25 pages, 4 Tables, no figures; v2: minor changes and corrections,
Ref. adde
Symmetric Spaces in Supergravity
We exploit the relation among irreducible Riemannian globally symmetric
spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions.
IRGS appear as scalar manifolds of the theories, as well as moduli spaces of
the various classes of solutions to the classical extremal black hole Attractor
Equations. Relations with Jordan algebras of degree three and four are also
outlined.Comment: 1+23 pages, 15 Tables. Contribution to the Proceedings of the
Conference "Symmetry in Mathematics and Physics", 18-20 Jan. 2008, IPAM
(UCLA), in celebration of V. S. Varadarajan's 70th Birthda
A Kind of Magic
We introduce the extended Freudenthal-Rosenfeld-Tits magic square based on
six algebras: the reals , complexes , ternions
, quaternions , sextonions and octonions
. The ternionic and sextonionic rows/columns of the magic square
yield non-reductive Lie algebras, including
. It is demonstrated that the
algebras of the extended magic square appear quite naturally as the symmetries
of supergravity Lagrangians. The sextonionic row (for appropriate choices of
real forms) gives the non-compact global symmetries of the Lagrangian for the
maximal , magic and magic
non-supersymmetric theories, obtained by dimensionally reducing the
parent theories on a circle, with the graviphoton left undualised. In
particular, the extremal intermediate non-reductive Lie algebra
(which is not a
subalgebra of ) is the non-compact global symmetry algebra
of , supergravity as obtained by dimensionally reducing
, supergravity with symmetry on a
circle. The ternionic row (for appropriate choices of real forms) gives the
non-compact global symmetries of the Lagrangian for the maximal
, magic and magic non-supersymmetric theories
obtained by dimensionally reducing the parent theories on a circle. In
particular, the Kantor-Koecher-Tits intermediate non-reductive Lie algebra
is the non-compact global
symmetry algebra of , supergravity as obtained by
dimensionally reducing , supergravity with
symmetry on a circle.Comment: 38 pages. Reference added and minor corrections mad
4d/5d Correspondence for the Black Hole Potential and its Critical Points
We express the d=4, N=2 black hole effective potential for cubic holomorphic
F functions and generic dyonic charges in terms of d=5 real special geometry
data. The 4d critical points are computed from the 5d ones, and their relation
is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of
attractors and the respective entropies. These are related by simple formulae,
interpolating between four and five dimensions, depending on the volume modulus
and on the 4d magnetic (or electric) charges, and holding true also for generic
field configurations and for non-symmetric cubic geometries.Comment: 1+24 pages; v2: references added, minor improvements; v3: further
minor improvements and clarification
Maurer-Cartan Equations and Black Hole Superpotentials in N =8 Supergravity
We retrieve the non-BPS extremal black hole superpotential of N=8, d=4
supergravity by using the Maurer-Cartan equations of the symmetric space
E_7(7)/SU(8). This superpotential was recently obtained with different 3- and
4-dimensional techniques. The present derivation is independent on the
reduction to d=3.Comment: 1+22 page
Extremal Black Hole and Flux Vacua Attractors
These lectures provide a pedagogical, introductory review of the so-called
Attractor Mechanism (AM) at work in two different 4-dimensional frameworks:
extremal black holes in N=2 supergravity and N=1 flux compactifications. In the
first case, AM determines the stabilization of scalars at the black hole event
horizon purely in terms of the electric and magnetic charges, whereas in the
second context the AM is responsible for the stabilization of the universal
axion-dilaton and of the (complex structure) moduli purely in terms of the RR
and NSNS fluxes. Two equivalent approaches to AM, namely the so-called
``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail
in both frameworks, whose analogies and differences are discussed. Also a
stringy analysis of both frameworks (relying on Hodge-decomposition techniques)
is performed, respectively considering Type IIB compactified on and
its orientifolded version, associated with . Finally, recent results on the U-duality orbits and
moduli spaces of non-BPS extremal black hole attractors in , d=4 supergravities are reported.Comment: 1+74 pages, 2 Tables. Contribution to the Proceedings of the Winter
School on Attractor Mechanism 2006 (SAM2006), 20-24 March 2006, INFN-LNF,
Frascati, Ital
Freudenthal Dual Lagrangians
The global U-dualities of extended supergravity have played a central role in
differentiating the distinct classes of extremal black hole solutions. When the
U-duality group satisfies certain algebraic conditions, as is the case for a
broad class of supergravities, the extremal black holes enjoy a further
symmetry known as Freudenthal duality (F-duality), which although distinct from
U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by
adopting the doubled Lagrangian formalism, F-duality, defined on the doubled
field strengths, is not only a symmetry of the black hole solutions, but also
of the equations of motion themselves. A further role for F-duality is
introduced in the context of world-sheet actions. The Nambu-Goto world-sheet
action in any (t, s) signature spacetime can be written in terms of the F-dual.
The corresponding field equations and Bianchi identities are then related by
F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the
world-sheet. An equivalent polynomial "Polyakov- type" action is introduced
using the so-called black hole potential. Such a construction allows for
actions invariant under all groups of type E7, including E7 itself, although in
this case the stringy interpretation is less clear.Comment: 1+16 pages, 1 Table, updated to match published versio
Non-BPS Attractors in 5d and 6d Extended Supergravity
We connect the attractor equations of a certain class of N=2, d=5
supergravities with their (1,0), d=6 counterparts, by relating the moduli space
of non-BPS d=5 black hole/black string attractors to the moduli space of
extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special
symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat
directions of the black object potential corresponding to vanishing eigenvalues
of its Hessian matrix. In the case N = 4, we study the relation to the (2,0),
d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in
N=8, d=5 supergravity as well as the interconnection among the corresponding
charge orbits.Comment: 1+27 page
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