Exact self-duality in a modified Skyrme model

We propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the couplings of the components of the Maurer-Cartan form of the Skyrme model is made by a non-constant symmetric matrix, instead of the usual Killing form of the SU(2) Lie algebra. The introduction of such a matrix make the self-duality equations conformally invariant in three space dimensions, even though it may break the global internal symmetries of the original Skyrme model. For the case where that matrix is proportional to the identity we show that the theory possesses exact self-dual Skyrmions of unity topological charges.Comment: 12 pages, no figure

Global-String and Vortex Superfluids in a Supersymmetric Scenario

The main goal of this work is to investigate the possibility of finding the supersymmetric version of the U(1)-global string model which behaves as a vortex-superfluid. To describe the superfluid phase, we introduce a Lorentz-symmetry breaking background that, in an approach based on supersymmetry, leads to a discussion on the relation between the violation of Lorentz symmetry and explicit soft supersymmetry breakings. We also study the relation between the string configuration and the vortex-superfluid phase. In the framework we settle down in terms of superspace and superfields, we actually establish a duality between the vortex degrees of freedom and the component fields of the Kalb-Ramond superfield. We make also considerations about the fermionic excitations that may appear in connection with the vortex formation.Comment: 9 pages. This version presented the relation between Lorentz symmetry violation by the background and the appearance of terms that explicitly break SUS

On the Benjamini--Hochberg method

We investigate the properties of the Benjamini--Hochberg method for multiple testing and of a variant of Storey's generalization of it, extending and complementing the asymptotic and exact results available in the literature. Results are obtained under two different sets of assumptions and include asymptotic and exact expressions and bounds for the proportion of rejections, the proportion of incorrect rejections out of all rejections and two other proportions used to quantify the efficacy of the method.Comment: Published at http://dx.doi.org/10.1214/009053606000000425 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hopf solitons and area preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere. The model possesses exact soliton solutions with non trivial Hopf topological charges, and infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area preserving diffeomorphisms of the sphere. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.Comment: 6 pages, LaTe

Charge and CP symmetry breaking in two Higgs doublet models

We show that, for the most generic model with two Higgs doublets possessing a minimum that preserves the $U(1)_{em}$ symmetry, charge breaking (CB) cannot occur. If CB does not occur, the potential could have two different minima, and there is in principle no general argument to show which one is the deepest. The depth of the potential at a stationary point that breaks CB or CP, relative to the $U(1)_{em}$ preserving minimum, is proportional to the squared mass of the charged or pseudoscalar Higgs, respectively

Exact Self-Dual Skyrmions

We introduce a Skyrme type model with the target space being the 3-sphere S^3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.Comment: 14 pages, 3 figures, a reference adde