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

Chaos from Symmetry: Navier Stokes equations, Beltrami fields and the Universal Classifying Crystallographic Group

In this report-article, the general setup to classify and construct Arnold-Beltrami Flows on three-dimensional torii, previously introduced by one of us, is further pursued. The idea of a Universal Classifying Group (UCG) is improved. In particular, we construct for the first time such group for the hexagonal lattice. Mastering the cubic and hexagonal instances, we can cover all cases. We upgrade Beltrami flows to a special type of periodic solutions of the NS equations, presenting the relation between the classification of these flows with the classification of contact structures. The recent developments in contact and symplectic geometry, considering singular contact structures, in the framework of b-manifolds, is also reviewed and we show that the choice of the critical surface for the b-deformation seems to be strongly related to its group-theoretical structures. This opens directions of investigation towards a classification of the critical surfaces or boundaries in terms of the UCG and subgroups. Furthermore, as a result of this research programme a complete set of MATHEMATICA Codes (for the cubic and hexagonal cases) have been produced that are able to construct Beltrami Flows with an arbitrarily large number of parameters and analyze their hidden symmetry structures. Indeed the main goal is the systematic organization of the parameter space into group irreps. The two Codes are a further result, being the unavoidable basis for further investigations. The presented exact solutions illustrate the new conceptions and ideas here discussed. The main message is: the more symmetric is the Beltrami Flow, the highest the probability of an on-set of chaotic trajectories. In various applications we need chaos on small scales and a more orderly motion on larger ones. Merging elementary chaotic solutions with large directional ordered flows is the target for future research.Comment: LaTeX source, 152 pages and 69 figures. arXiv admin note: substantial text overlap with arXiv:1501.0460

Theory of Superdualities and the Orthosymplectic Supergroup

We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO(m,m) duality for D=2 sigma models and the Sp(2n) duality for D=4 sigma models is the orthosymplectic duality OSp(m,m|2 n). We study the implications of this and we derive the most general D=2 sigma model, coupled to fermionic and bosonic one-forms, with such dualities. To achieve this we generalize Gaillard-Zumino analysis to orthosymplectic dualities, which requires to define embedding of the superisometry group of the target space into the duality group. We finally discuss the recently proposed fermionic dualities as a by-product of our construction.Comment: 35 pages, LaTeX sourc