Non-abelian Eikonals

A functional formulation and partial solution is given of the non-abelian eikonal problem associated with the exchange of non-interacting, charged or colored bosons between a pair of fermions, in the large $s$/small $t$ limit. A simple, functional ``contiguity" prescription is devised for extracting those terms which exponentiate, and appear to generate the leading, high-energy behavior of each perturbative order of this simplest non-abelian eikonal function; the lowest non-trivial order agrees with the corresponding SU(N) perturbative amplitude, while higher-order contributions to this eikonal generate an ``effective Reggeization" of the exchanged bosons, resembling previous results for the perturbative amplitude. One exact and several approximate examples are given, including an application to self-energy radiative corrections. In particular, for this class of graphs and to all orders in the coupling, we calculate the leading-log eikonal for SU(2). Based on this result, we conjecture the form of the eikonal scattering amplitude for SU(N).Comment: 19 pages, late

Singular del Pezzo fibrations and birational rigidity

A known conjecture of Grinenko in birational geometry asserts that a Mori fibre space with the structure of del Pezzo fibration of low degree is birationally rigid if and only if its anticanonical class is an interior point in the cone of mobile divisors. The conjecture is proved to be true for smooth models (with a generality assumption for degree 3). It is speculated that the conjecture holds for, at least, Gorenstein models in degree 1 and 2. In this article, I present a (Gorenstein) counterexample in degree 2 to this conjecture.Comment: This is essentially a more detailed version of the second section of arXiv:1310.5548. To appear in the proceedings of the conference 'Groups of Automorphisms in Birational and Affine Geometry', held in Trento, Italy, 201

Exact time-reversal focusing of acoustic and quantum excitations in open cavities: The perfect inverse filter

The time-reversal mirror (TRM) prescribes the reverse playback of a signal to focalize an acoustic excitation as a Loschmidt echo. In the quantum domain, the perfect inverse filter (PIF) processes this signal to ensure an exact reversion provided that the excitation originated outside the cavity delimited by the transducers. We show that PIF takes a simple form when the initial excitation is created inside this cavity. This also applies to the acoustical case, where it corrects the TRM and improves the design of an acoustic bazooka. We solve an open chaotic cavity modeling a quantum bazooka and a simple model for a Helmholtz resonator, showing that the PIF becomes decisive to compensate the group velocities involved in a highly localized excitation and to achieve subwavelength resolution.Comment: 6 pages, 2 figure

Thermodynamics of Rotating Black Branes in Gauss-Bonnet-Born-Infeld Gravity

Considering both the Gauss-Bonnet and the Born-Infeld terms, which are on similar footing with regard to string corrections on the gravity side and electrodynamic side, we present a new class of rotating solutions in Gauss-Bonnet gravity with $k$ rotation parameters in the presence of a nonlinear electromagnetic field. These solutions, which are asymptotically anti-de Sitter in the presence of cosmological constant, may be interpreted as black brane solutions with inner and outer event horizons, an extreme black brane or naked singularity provided the metric parameters are chosen suitably. We calculate the finite action and conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the Gauss-Bonnet parameter. We also compute the temperature, the angular velocities, the electric charge and the electric potential. Then, we calculate the entropy of the black brane through the use of Gibbs-Duhem relation and show that it obeys the area law of entropy. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the charge, and show that the conserved and thermodynamic quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis in both the canonical and grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field has no effect on the stability of the black branes, and they are stable in the whole phase space.Comment: 17 pages, one figur

A magnetic cycle of tau Bootis? The coronal and chromospheric view

Tau Bootis is a late F-type main sequence star orbited by a Hot Jupiter. During the last years spectropolarimetric observations led to the hypothesis that this star may host a global magnetic field that switches its polarity once per year, indicating a very short activity cycle of only one year duration. In our ongoing observational campaign, we have collected several X-ray observations with XMM-Newton and optical spectra with TRES/FLWO in Arizona to characterize tau Boo's corona and chromosphere over the course of the supposed one-year cycle. Contrary to the spectropolarimetric reconstructions, our observations do not show indications for a short activity cycle.Comment: 4 pages, 2 figures, appeared in Astronomical Notes 333, 1, 26-29 (2012