Superintegrability in a two-dimensional space of nonconstant curvature

A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions. This is done by examining in detail one of the spaces of revolution found by G. Koenigs. We determine that there are essentially three distinct potentials which when added to the free Hamiltonian of this space have this type of superintegrability. Separation of variables for the associated Hamilton–Jacobi and Schrödinger equations is discussed. The classical and quantum quadratic algebras associated with each of these potentials are determined

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.Comment: Latex, 15 page

Magnetic field induced chiral particle-hole condensates

We demonstrate that a chiral particle-hole condensate is always induced by a number-conserving ground state of non-zero angular momentum in the presence of a magnetic field. The magnetic interaction originates from the coupling with the intrinsic orbital moment of the chiral state when the field is applied perpendicularly to the plane. According to our numerical results the induction mechanism is practically temperature independent providing robustness to these states up to high temperatures. This opens the door for manipulating the anomalous Hall response resulting from this intricate class of states for technological applications while it also suggests that chiral particle-hole condensates may be hidden in various complex materials.Comment: This is the final version accepted by Phys. Rev. B (Brief Reports

Jets and outflows in Radio Galaxies: implications for AGN feedback

One of the main debated astrophysical problems is the role of the AGN feedback in galaxy formation. It is known that massive black holes have a profound effect on the formation and evolution of galaxies, but how black holes and galaxies communicate is still an unsolved problem. For Radio Galaxies, feedback studies have mainly focused on jet/cavity systems in the most massive and X-ray luminous galaxy clusters. The recent high-resolution detection of warm absorbers in some Broad Line Radio Galaxies allow us to investigate the interplay between the nuclear engine and the surrounding medium from a different perspective. We report on the detection of warm absorbers in two Broad Line Radio Galaxies, 3C 382 and 3C 390.3, and discuss the physical and energetic properties of the absorbing gas. Finally, we attempt a comparison between radio-loud and radio-quiet outflows.Comment: To be published in the proceedings of High Energy Phenomena in Relativistic Outflows III (HEPRO III, IJMPCS). 4 pages, 2 figure

Multi-instanton and string loop corrections in toroidal orbifold models

We analyze N=2 (perturbative and non-perturbative) corrections to the effective theory in type I orbifold models where a dual heterotic description is available. These corrections may play an important role in phenomenological scenarios. More precisely, we consider two particular compactifications: the Bianchi-Sagnotti-Gimon-Polchinski orbifold and a freely-acting Z_2 x Z_2 orbifold with N=1 supersymmetry and gauge group SO(q) x SO(32-q). By exploiting perturbative calculations of the physical gauge couplings on the heterotic side, we obtain multi-instanton and one-loop string corrections to the K\"ahler potential and the gauge kinetic function for these models. The non-perturbative corrections appear as sums over relevant Hecke operators, whereas the one-loop correction to the K\"ahler potential matches the expression proposed in [1,2]. We argue that these corrections are universal in a given class of models where target-space modular invariance (or a subgroup of it) holds.Comment: 37 pages, 3 figure