94 research outputs found
The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities
Relying on the geometrical set up of Special K\"ahler Geometry and
Quaternionic Geometry, which I discussed at length in my Lectures at the 1995
edition of this Spring School, I present here the recently obtained fully
general form of N=2 supergravity with completely arbitrary couplings. This
lagrangian has already been used in the literature to obtain various results:
notably the partial breaking of supersymmetry and various extremal black--hole
solutions. My emphasis, however, is only on providing the reader with a
completely explicit and ready to use component expression of the supergravity
action. All the details of the derivation are omitted but all the definitions
of the items entering the lagrangian and the supersymmetry transformation rules
are given.Comment: 11 pages, LaTeX espcrc2, Seminar at Trieste Spring School 199
Integrability of Supergravity Black Holes and New Tensor Classifiers of Regular and Nilpotent Orbits
In this paper we apply in a systematic way a previously developed integration
algorithm of the relevant Lax equation to the construction of spherical
symmetric, asymptotically flat black hole solutions of N=2 supergravities with
symmetric Special Geometry. Our main goal is the classification of these
black-holes according to the H*-orbits in which the space of possible Lax
operators decomposes, H* being the isotropy group of scalar manifold
originating from time-like dimensional reduction of supergravity from D=4 to
D=3 dimensions. The main result of our investigation is the construction of
three universal tensors, extracted from quadratic and quartic powers of the Lax
operator, that are capable of classifying both regular and nilpotent H* orbits
of Lax operators. Our tensor based classification is compared, in the case of
the simple one-field model S^3, to the algebraic classification of nilpotent
orbits and it is shown to provide a simple and practical discriminating method.
We present a detailed analysis of the S^3 model and its black hole solutions,
discussing the Liouville integrability of the corresponding dynamical system.
By means of the Kostant-representation of a generic Lie algebra element, we
were able to develop an algorithm which produces the necessary number of
hamiltonians in involution required by Liouville integrability of generic
orbits. The degenerate orbits correspond to extremal black-holes and are
nilpotent. We analyze these orbits in some detail working out different
representatives thereof and showing that the relation between H* orbits and
critical points of the geodesic potential is not one-to-one. Finally we present
the conjecture that our newly identified tensor classifiers are universal and
able to label all regular and nilpotent orbits in all homogeneous symmetric
Special Geometries.Comment: Analysis of nilpotent orbits in terms of tensor classifiers in
section 8.1 corrected. Table 1 corrected. Discussion in section 11 extende
Superstrings on AdS_4 x CP^3 from Supergravity
We derive from a general formulation of pure spinor string theory on type IIA
backgrounds the specific form of the action for the AdS_4 x P^3 background. We
provide a complete geometrical characterization of the structure of the
superfields involved in the action.Comment: 32 pages, Latex, no figure
Optimizing local protocols implementing nonlocal quantum gates
We present a method of optimizing recently designed protocols for
implementing an arbitrary nonlocal unitary gate acting on a bipartite system.
These protocols use only local operations and classical communication with the
assistance of entanglement, and are deterministic while also being "one-shot",
in that they use only one copy of an entangled resource state. The optimization
is in the sense of minimizing the amount of entanglement used, and it is often
the case that less entanglement is needed than with an alternative protocol
using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546
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