146 research outputs found
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
The -linked complex Minkowski space, its real forms and deformed isometry groups
We establish duality between real forms of the quantum deformation of the
4-dimensional orthogonal group studied by Fioresi et al. and the classification
work made by Borowiec et al.. Classically these real forms are the isometry
groups of equipped with Euclidean, Kleinian or Lorentzian
metric. A general deformation, named -linked, of each of these spaces is
then constructed, together with the coaction of the corresponding isometry
group.Comment: 25 pages, discussion improved, bibliography update
d=4 Attractors, Effective Horizon Radius and Fake Supergravity
We consider extremal black hole attractors (both BPS and non-BPS) for N=3 and
N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled
N=3 theory are similar to attractors in N=2 supergravity minimally coupled to
Abelian vector multiplets. On the other hand, N=5 attractors are similar to
attractors in N=4 pure supergravity, and in such theories only 1\N-BPS
non-degenerate solutions exist. All the above mentioned theories have a simple
interpretation in the first order (fake supergravity) formalism. Furthermore,
such theories do not have a d=5 uplift. Finally we comment on the "duality"
relations among the attractor solutions of N\geq2 supergravities sharing the
same full bosonic sector.Comment: 1+47 pages, 2 Tables. v2: Eqs. (2.3),(2.4) and Footnote 3 added;
minor cosmetic changes; to appear in PR
Four-qubit entanglement from string theory
We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references
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Iwasawa N=8 Attractors
Starting from the symplectic construction of the Lie algebra e_7(7) due to
Adams, we consider an Iwasawa parametrization of the coset E_7(7)/SU(8), which
is the scalar manifold of N=8, d=4 supergravity. Our approach, and the manifest
off-shell symmetry of the resulting symplectic frame, is determined by a
non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E_7(7). In
absence of gauging, we utilize the explicit expression of the Lie algebra to
study the origin of E_7(7)/SU(8) as scalar configuration of a 1/8-BPS extremal
black hole attractor. In such a framework, we highlight the action of a U(1)
symmetry spanning the dyonic 1/8-BPS attractors. Within a suitable
supersymmetry truncation allowing for the embedding of the Reissner-Nordstrom
black hole, this U(1) is interpreted as nothing but the global R-symmetry of
pure N=2 supergravity. Moreover, we find that the above mentioned U(1) symmetry
is broken down to a discrete subgroup Z_4, implying that all 1/8-BPS Iwasawa
attractors are non-dyonic near the origin of the scalar manifold. We can trace
this phenomenon back to the fact that the Cartan subalgebra of SL(8,R) used in
our construction endows the symplectic frame with a manifest off-shell
covariance which is smaller than SL(8,R) itself. Thus, the consistence of the
Adams-Iwasawa symplectic basis with the action of the U(1) symmetry gives rise
to the observed Z_4 residual non-dyonic symmetry.Comment: 1+26 page
Intersecting Attractors
We apply the entropy formalism to the study of the near-horizon geometry of
extremal black p-brane intersections in D>5 dimensional supergravities. The
scalar flow towards the horizon is described in terms an effective potential
given by the superposition of the kinetic energies of all the forms under which
the brane is charged. At the horizon active scalars get fixed to the minima of
the effective potential and the entropy function is given in terms of U-duality
invariants built entirely out of the black p-brane charges. The resulting
entropy function reproduces the central charges of the dual boundary CFT and
gives rise to a Bekenstein-Hawking like area law. The results are illustrated
in the case of black holes and black string intersections in D=6, 7, 8
supergravities where the effective potentials, attractor equations, moduli
spaces and entropy/central charges are worked out in full detail.Comment: 1+41 pages, 2 Table
Two-centered magical charge orbits
We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the
horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product , known to control the mutual nonlocality of the two centers
The common NOD2/CARD15 variant P268S in patients with non-infectious uveitis: A cohort study
Background: The etiology of Autoimmune chronic uveitis (ACU) is still unknown; NOD2/CARD15 gene mutations are responsible for the Blau Syndrome and can induce uveitis in animal models. Presentation of the hypothesis: Aim of our study was to assess if NOD2/CARD15 variants have a role in the etiology or in the clinical course of patients with ACU, either idiopathic or associated with other inflammatory diseases. Testing the hypothesis: We consecutively enrolled 25 patients (19 pediatric and 6 adults) affected with ACU. For each patient medical history was reviewed and clinical data were recorded. Allelic and genotypic frequencies of NOD2/CARD15 variations were calculated in patients and matched with those of 25 healthy controls. The statistical analysis was performed. Fifteen patients showed the polymorphism P268S/SNP5 (SNP rs2066842) as heterozygous carriers while two patients were homozygous for the same polymorphism; one patient carried also the variant c647 18-16 TCT on intron 3, not previously reported in the literature. Statistical analysis for NOD2/CARD15 genotyping showed significant differences between patients and controls for allelic frequencies (p=0.04, OR: 4.03, 95 %; CI=1.2-13.5) but not for genotypic frequencies. We could not identify a significant phenotype-genotype correlation. Implications of the hypothesis: In our cohort of Italian patients, the NOD2/CARD15 common variant P268S/SNP5 could potentially be significantly associated with ACU
Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
We derive the U-duality charge orbits, as well as the related moduli spaces,
of "large" and "small" extremal black holes in non-maximal ungauged
Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5
space-time dimensions. The stabilizer groups of the various classes of orbits
are obtained by determining and solving suitable U-invariant sets of
constraints, both in "bare" and "dressed" charges bases, with various methods.
After a general treatment of attractors in real special geometry (also
considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2
Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal
(N=4) matter-coupled supergravity is also studied in this context.Comment: 1+63 pages, 6 Table
Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants
We classify 2-center extremal black hole charge configurations through
duality-invariant homogeneous polynomials, which are the generalization of the
unique invariant quartic polynomial for single-center black holes based on
homogeneous symmetric cubic special Kaehler geometries. A crucial role is
played by an horizontal SL(p,R) symmetry group, which classifies invariants for
p-center black holes. For p = 2, a (spin 2) quintet of quartic invariants
emerge. We provide the minimal set of independent invariants for the rank-3 N =
2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st^2
and rank-1 t^3 models; these models respectively exhibit seven, six and five
independent invariants. We also derive the polynomial relations among these and
other duality invariants. In particular, the symplectic product of two charge
vectors is not independent from the quartic quintet in the t^3 model, but
rather it satisfies a degree-16 relation, corresponding to a quartic equation
for the square of the symplectic product itself.Comment: 1+31 pages; v2: amendments in Sec. 9, App. C added, other minor
refinements, Refs. added; v3: Ref. added, typos fixed. To appear on
J.Math.Phy
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