On the Topology of the Inflaton Field in Minimal Supergravity Models

We consider global issues in minimal supergravity models where a single field inflaton potential emerges. In a particular case we reproduce the Starobinsky model and its description dual to a certain formulation of R+R^2 supergravity. For definiteness we confine our analysis to spaces at constant curvature, either vanishing or negative. Five distinct models arise, two flat models with respectively a quadratic and a quartic potential and three based on the SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way and they turn out to be a crucial ingredient in order to describe the de Sitter inflationary phase of the Starobinsky model.Comment: 31 pages, LaTex, 7 eps figures, 2 table

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

Bruhat Order in the Full Symmetric sln\mathfrak{sl}_n Toda Lattice on Partial Flag Space

In our previous paper [Comm. Math. Phys. 330 (2014), 367-399] we described the asymptotic behaviour of trajectories of the full symmetric $\mathfrak{sl}_n$ Toda lattice in the case of distinct eigenvalues of the Lax matrix. It turned out that it is completely determined by the Bruhat order on the permutation group. In the present paper we extend this result to the case when some eigenvalues of the Lax matrix coincide. In that case the trajectories are described in terms of the projection to a partial flag space where the induced dynamical system verifies the same properties as before: we show that when $t\to\pm\infty$ the trajectories of the induced dynamical system converge to a finite set of points in the partial flag space indexed by the Schubert cells so that any two points of this set are connected by a trajectory if and only if the corresponding cells are adjacent. This relation can be explained in terms of the Bruhat order on multiset permutations

Hybrid Optical Fibers – An Innovative Platform for In‐Fiber Photonic Devices

The field of hybrid optical fibers is one of the most active research areas in current fiber optics and has the vision of integrating sophisticated materials inside fibers, which are not traditionally used in fiber optics. Novel in-fiber devices with unique properties have been developed, opening up new directions for fiber optics in fields of critical interest in modern research, such as biophotonics, environmental science, optoelectronics, metamaterials, remote sensing, medicine, or quantum optics. Here the recent progress in the field of hybrid optical fibers is reviewed from an application perspective, focusing on fiber-integrated devices enabled by including novel materials inside polymer and glass fibers. The topics discussed range from nanowire-based plasmonics and hyperlenses, to integrated semiconductor devices such as optoelectronic detectors, and intense light generation unlocked by highly nonlinear hybrid waveguides