6,686 research outputs found
Orbits of Exceptional Groups, Duality and BPS States in String Theory
We give an invariant classification of orbits of the fundamental
representations of exceptional groups and which classify
BPS states in string and M theories toroidally compactified to d=4 and d=5. The
exceptional Jordan algebra and the exceptional Freudenthal triple system and
their cubic and quartic invariants play a major role in this classification.
The cubic and quartic invariants correspond to the black hole entropy in d=5
and d=4, respectively. The classification of BPS states preserving different
numbers of supersymmetries is in close parallel to the classification of the
little groups and the orbits of timelike, lightlike and space-like vectors in
Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein
supergravity theories in d=4 and d=5 with symmetric space geometries are also
classified including the exceptional N=2 theory that has and
as its symmety in the respective dimensions.Comment: New references and two tables added, a new section on the orbits of
N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 included and some
minor changes were made in other sections. 17 pages. Latex fil
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
Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy
In these lectures we give a geometrical formulation of N-extended
supergravities which generalizes N=2 special geometry of N=2 theories. In all
these theories duality symmetries are related to the notion of "flat symplectic
bundles" and central charges may be defined as "sections" over these bundles.
Attractor points giving rise to "fixed scalars" of the horizon geometry and
Bekenstein-Hawking entropy formula for extremal black-holes are discussed in
some details.Comment: Based on lectures given by S. Ferrara at the 5th Winter School on
Mathematical Physics held at the Asia Pacific Center for Theoretical Physics,
Seul (Korea), February 199
On Invariant Structures of Black Hole Charges
We study "minimal degree" complete bases of duality- and "horizontal"-
invariant homogeneous polynomials in the flux representation of two-centered
black hole solutions in two classes of D=4 Einstein supergravity models with
symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R)
"horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled
theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis
is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting
maximal manifest covariance) and until order six in the fluxes included. The
second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes
N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by
the pseudo-unitary group U(r,s) (related to complex flux representations).
Finally, we comment on the formulation of special Kaehler geometry in terms of
"generalized" groups of type E7.Comment: 1+24 pages; 1 Table. v2 : Eqs. (1.2) and (1.3) added; Eq. (2.87)
change
Branes, central charges and U-duality invariant BPS conditions
In extended supergravity theories there are -brane solutions preserving
different numbers of supersymmetries, depending on the charges, the spacetime
dimension and the number of original supersymmetries (8, 16 or 32). We find
U-duality invariant conditions on the quantized charges which specify the
number of supersymmetries preserved with a particular charge configuration.
These conditions relate U-duality invariants to the picture of intersecting
branes. The analysis is carried out for all extended supergravities with 16 or
32 supersymmetries in various dimensions.Comment: 15 pages, no figures, typos correcte
On Black Attractors in 8D and Heterotic/Type IIA Duality
Motivated by the study of black attractors in 8D supergravity with 16
supersymmetries, we use the field theory approach and 8D supersymmetry with non
trivial central charges to shed light on the exact duality between heterotic
string on T^2 and type IIA on real connected and compact surfaces {\Sigma}2. We
investigate the two constraints that should be obeyed by {\Sigma}2 and give
their solutions in terms of intersecting 2-cycles as well their classification
using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that
the moduli space of these dual theories is given by
SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge
symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases
r=-2,-1,0 as well as other features are also investigated.Comment: LaTex, 18 pages, 2 figures, To appear in JHE
On Central Charges and Hamiltonians for 0-brane dynamics
We consider general properties of central charges of zero branes and
associated duality invariants, in view of their double role, on the bulk and on
the world volume (quantum-mechanical) theory. A detailed study of the BPS
condition for the mass spectrum arising from toroidal compactifications is
given for 1/2, 1/4 and 1/8 BPS states in any dimensions. As a byproduct, we
retreive the U-duality invariant conditions on the charge (zero mode) spectrum
and the orbit classification of BPS states preserving different fractions of
supersymmetry. The BPS condition for 0-branes in theories with 16
supersymmetries in any dimension is also discussed.Comment: 23 pages, latex fil
Manned Venus Flyby
This study is one of several being conducted at Bellcomm and in Manned Space Flight whose purpose is to give guidance to the Apollo Applications Program's technical objectives by focusing on a longer range goal. The assumed mission in this case is a three-man flyby of Venus launched in November, 1973 on a single standard Saturn V. The selected flight configuration includes a Command and Service Module similar in some respects to Apollo, an Environmental Support Module which occupies the adapter area and a spent S-IVB stage which is utilized for habitable volume and structural support of a solar cell electrical power system. The total injected weight, 106,775 lbs., is within the capability of a single Saturn V of the early 1970's. The study is focused on the selection of subsystem technologies appropriate to long duration flight. The conclusions are reported in terms of the technical characteristics to be achieved as part of the Apollo Applications Program's long duration objectives
Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
We determine explicit orbit representatives of reducible Jordan algebras and
of their corresponding Freudenthal triple systems. This work has direct
application to the classification of extremal black hole solutions of N = 2, 4
locally supersymmetric theories of gravity coupled to an arbitrary number of
Abelian vector multiplets in D = 4, 5 space-time dimensions.Comment: 18 pages. Updated to match published versio
On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
We investigate supergroups with Grassmann parameters replaced by odd Clifford
parameters. The connection with non-anticommutative supersymmetry is discussed.
A Berezin-like calculus for odd Clifford variables is introduced. Fermionic
covariant derivatives for supergroups with odd Clifford variables are derived.
Applications to supersymmetric quantum mechanics are made. Deformations of the
original supersymmetric theories are encountered when the fermionic covariant
derivatives do not obey the graded Leibniz property. The simplest non-trivial
example is given by the N=2 SQM with a real multiplet and a cubic
potential. The action is real. Depending on the overall sign ("Euclidean" or
"Lorentzian") of the deformation, a Bender-Boettcher pseudo-hermitian
hamiltonian is encountered when solving the equation of motion of the auxiliary
field. A possible connection of our framework with the Drinfeld twist
deformation of supersymmetry is pointed out.Comment: Final version to be published in Int. J. Mod. Phys. A; 20 page
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