Wick type deformation quantization of Fedosov manifolds

A coordinate-free definition for Wick-type symbols is given for symplectic manifolds by means of the Fedosov procedure. The main ingredient of this approach is a bilinear symmetric form defined on the complexified tangent bundle of the symplectic manifold and subject to some set of algebraic and differential conditions. It is precisely the structure which describes a deviation of the Wick-type star-product from the Weyl one in the first order in the deformation parameter. The geometry of the symplectic manifolds equipped by such a bilinear form is explored and a certain analogue of the Newlander-Nirenberg theorem is presented. The 2-form is explicitly identified which cohomological class coincides with the Fedosov class of the Wick-type star-product. For the particular case of K\"ahler manifold this class is shown to be proportional to the Chern class of a complex manifold. We also show that the symbol construction admits canonical superextension, which can be thought of as the Wick-type deformation of the exterior algebra of differential forms on the base (even) manifold. Possible applications of the deformed superalgebra to the noncommutative field theory and strings are discussed.Comment: 20 pages, no figure

Deviation From \Lambda CDM With Cosmic Strings Networks

In this work, we consider a network of cosmic strings to explain possible deviation from \Lambda CDM behaviour. We use different observational data to constrain the model and show that a small but non zero contribution from the string network is allowed by the observational data which can result in a reasonable departure from \Lambda CDM evolution. But by calculating the Bayesian Evidence, we show that the present data still strongly favour the concordance \Lambda CDM model irrespective of the choice of the prior.Comment: 15 Pages, Latex Style, 4 eps figures, Revised Version, Accepted for publication in European Physical Journal

The Peculiar-Velocity-Field in Structure Formation Theories with Cosmic Strings

We investigate the peculiar velocity field due to long cosmic strings in several cosmological models and analyse the influence of a nonscaling behaviour of the string network, which is expected in open cosmological models or models with a cosmological constant. It is shown that the deviation of the propability distribution of the peculiar velocity field from the normal distribution is only weak in all models. It is further argued that one can not necessarily obtain the parameter $\beta=\Omega_{0}^{0.6}/b$ from density and velocity fields, where $\Omega_0$ is the density parameter and $b$ the linear biasing parameter, if cosmic strings are responsible for structure formation in the universe. An explanation for this finding is given.Comment: 11 pages, 5 figure

Stability of string defects in models of non-Abelian symmetry breaking

In this paper we describe a new type of topological defect, called a homilia string, which is stabilized via interactions with the string network. Using analytical and numerical techniques, we investigate the stability and dynamics of homilia strings, and show that they can form stable electroweak strings. In SU(2)xU(1) models of symmetry breaking the intersection of two homilia strings is identified with a sphaleron. Due to repulsive forces, the homilia strings seperate, resulting in sphaleron annihilation. It is shown that electroweak homilia string loops cannot stabilize as vortons, which circumvents the adverse cosmological problems associated with stable loops. The consequences for GUT scale homilia strings are also discussed.Comment: 15 pages, revtex, with 8 figures. Submitted to PR

Deformed strings in the Heisenberg model

We investigate solutions to the Bethe equations for the isotropic S = 1/2 Heisenberg chain involving complex, string-like rapidity configurations of arbitrary length. Going beyond the traditional string hypothesis of undeformed strings, we describe a general procedure to construct eigenstates including strings with generic deformations, discuss general features of these solutions, and provide a number of explicit examples including complete solutions for all wavefunctions of short chains. We finally investigate some singular cases and show from simple symmetry arguments that their contribution to zero-temperature correlation functions vanishes.Comment: 34 pages, 13 figure

Dynamical behavior and Jacobi stability analysis of wound strings

We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of $\mathbb{R}^2$, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an $S^2$ of constant radius $\mathcal{R}$. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective $(3+1)$-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.Comment: 46 pages, 26 figures, accepted for publication in EPJC; matches the published version. Updated references (v3