DUALITY AND CONFINEMENT IN THREE DIMENSIONAL YANG-MILLS THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 4827-4843 ◽  
Author(s):  
C. A. ARAGÃO de CARVALHO ◽  
E. C. MARINO ◽  
G. C. MARQUES ◽  
M. GOLDMAN de CASTRO
Keyword(s):  
Three Dimensional ◽  
Long Distance ◽  
Complex Scalar ◽  
Yang Mills ◽  
Local Complex ◽  
Symmetry Phase ◽  
Complex Scalar Field ◽  
Operator Realization ◽  
Distance Properties ◽  
General Method

We exploit the order-disorder duality existing between the Wilson loop operator W(c) of an SU (N) Yang-Mills theory, and a local complex scalar field ϕ of a theory with global Z(N) symmetry in 2 + 1 dimensions, in order to establish a general method for the computation of the correlation functions of W(c) within the framework of the dual ϕ field theory. An explicit operator realization of W(c) in terms of ϕ is obtained. An effective dual Lagrangian, Lϕ, is proposed to account for the long distance properties of the theory. It is shown that, for N = 2, 3, 4, 5 this dual theory is always in a completely broken Z(N) symmetry phase. An explicit computation shows that for these values of N <W(c)> has an area type behavior for the whole range of the parameters, meaning that the static quarks will be permanently confined.

scholarly journals QUARKS AS TOPOLOGICAL DEFECTS — OR, WHAT IS CONFINED INSIDE A HADRON?

1993 ◽  
Vol 08 (31) ◽  
pp. 5575-5604 ◽  
Author(s):  
A. KOVNER ◽  
B. ROSENSTEIN
Keyword(s):  
Magnetic Flux ◽  
Topological Charge ◽  
Domain Walls ◽  
Topological Defects ◽  
Complex Scalar ◽  
Yang Mills ◽  
Effective Lagrangian ◽  
Local Complex ◽  
Complex Scalar Field ◽  
The One

We present a picture of confinement based on representation of constituent quarks as pointlike topological defects. The topological charge carried by quarks and confined in hadrons is explicitly constructed in terms of Yang-Mills variables. In 2+1 dimensions we are able to construct a local complex scalar field V(x), in terms of which the topological charge is [Formula: see text]. The VEV of the field V in the confining phase is nonzero and the charge is the winding number corresponding to homotopy group π1(S1). Quarks carry the charge Q and therefore are topological solitons. The phase rotation of V is generated by the operator of magnetic flux. Unlike in QED, the U(1) magnetic flux is explicitly broken by the monopoles. This results in formation of a string between a quark and an antiquark. The effective Lagrangian for V is derived in models with adjoint and fundamental quarks. This topological mechanism of confinement is basically different from the one proposed by ’t Hooft in which the elementary objects are linelike domain walls. A baryon is described as a Y-shaped configuration of strings. In 3+1 dimensions the explicit expression for V, and therefore a detailed picture, is not available. However, assuming the validity of the same mechanism we point out several interesting qualitative consequences.

Field models

2021 ◽  
pp. 42-69
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Spinor Field ◽  
Vector Fields ◽  
Sigma Model ◽  
Complex Scalar ◽  
Yang Mills ◽  
Scalar Field Models ◽  
Complex Scalar Field ◽  
Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

scholarly journals A General Method for Transforming Nonphysical Configurations in BPS States

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
J. R. L. Santos ◽  
A. de Souza Dutra ◽  
O. C. Winter ◽  
R. A. C. Correa
Keyword(s):  
Scalar Field ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Cosmological Parameters ◽  
Topological Defects ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Bps States ◽  
General Method

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model. In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named nonphysical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.

scholarly journals A NEW QUANTUM VORTEX OPERATOR AND ITS CORRELATION FUNCTIONS

1995 ◽  
Vol 10 (30) ◽  
pp. 4311-4324 ◽  
Author(s):  
E.C. MARINO
Keyword(s):  
Correlation Functions ◽  
Three Dimensional ◽  
Higgs Field ◽  
Gauge Field Theories ◽  
Maxwell Theory ◽  
Long Distance ◽  
Absolute Value ◽  
Quantum Vortex ◽  
Symmetry Phase ◽  
Invariant Quantum

A new local and gauge-invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of an expansion around a constant absolute value of the Higgs field in the Abelian Higgs model. In the broken symmetry phase of the latter an explicit expression for the mass of the quantum vortices is obtained from the long distance exponential decay of the two-point function.

SOLITONS AND BUBBLES IN MODELS WITH CHERN-SIMONS TERM

1992 ◽  
Vol 07 (34) ◽  
pp. 3245-3254
Author(s):  
L. MASPERI
Keyword(s):  
Complex Scalar ◽  
Relativistic Limit ◽  
First Order ◽  
String Type ◽  
First Order Phase Transition ◽  
Symmetry Phase ◽  
Complex Scalar Field ◽  
First Order Phase ◽  
Chern Simons

It is shown that a gauge theory for complex scalar field with up to sextic self-interactions and a Chern-Simons term in 2+1 dimensions has solitons which may become bubbles of the stable broken-symmetry phase in a medium of the symmetric one producing the first order phase transition. In the non-relativistic limit scale invariance prevents the determination of an optimal bubble size. Possible extensions to 3 + 1 dimensions of bubbles of string type are indicated.

Noise reduction by combining smearing with multi-level integration methods

2014 ◽  
Vol 23 (06) ◽  
pp. 1460008 ◽  
Author(s):  
Ahmed S. Bakry ◽  
Xurong Chen ◽  
Pengming Zhang
Keyword(s):  
Three Dimensional ◽  
Error Reduction ◽  
Reduction Technique ◽  
Computational Time ◽  
Long Distance ◽  
Simultaneous Application ◽  
Yang Mills ◽  
Measuring Field ◽  
Multi Level ◽  
Key Features

In this paper, we propose an algorithm that combines the Lüscher–Weiss (LW) multi-level error reduction technique with three-dimensional gauge-field smoothing. The purpose of this algorithm is to reduce the noise and the computational time associated with measuring field correlators in the low temperature pure quantum chromodynamics (QCD), or the stringy regions of Yang–Mills theory in general. The simultaneous application of both link-blocking and path-integral factorization techniques is based on the observation that Monte Carlo updating of the three-dimensional smeared lattices preserves the key features of the long distance physics.

scholarly journals Gravitating Bubbles of Gluon Plasma above Deconfinement Temperature

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1668
Author(s):  
Yves Brihaye ◽  
Fabien Buisseret
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Gluon Plasma ◽  
Einstein Gravity ◽  
Spherically Symmetric ◽  
Boson Stars ◽  
Complex Scalar ◽  
Symmetric Potential ◽  
Yang Mills ◽  
Complex Scalar Field

The equation of state of SU(3) Yang–Mills theory can be modelled by an effective Z3−symmetric potential depending on the temperature and on a complex scalar field ϕ. Allowing ϕ to be dynamical opens the way to the study of spatially localized classical configurations of the scalar field. We first show that spherically symmetric static Q-balls exist in the range (1−1.21)×Tc, Tc being the deconfinement temperature. Then we argue that Q-holes solutions, if any, are unphysical within our framework. Finally, we couple our matter Lagrangian to Einstein gravity and show that spherically symmetric static boson stars exist in the same range of temperature. The Q-ball and boson-star solutions we find can be interpreted as “bubbles” of deconfined gluonic matter; their mean radius is always smaller than 10 fm.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

scholarly journals Using Externally Bonded CFRP to Repair a PCCP with Broken Wires under Combined Loads

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Kejie Zhai ◽  
Hongyuan Fang ◽  
Bing Fu ◽  
Fuming Wang ◽  
Benyue Hu
Keyword(s):  
Prestressed Concrete ◽  
Three Dimensional ◽  
Soil Pressure ◽  
Long Distance ◽  
Stress Strain ◽  
Wire Breakage ◽  
Water Pipelines ◽  
Externally Bonded ◽  
Prestressed Concrete Cylinder Pipe ◽  
Three Dimensional Finite Element

Prestressed concrete cylinder pipe (PCCP) is widely used for long-distance water pipelines throughout the world. However, prestressing wire breakage is the most common form of PCCP damage. For some pipelines that cannot be shut down, a new technique for in-service PCCP repair by externally bonding the pipe with layers of carbon fiber reinforced polymer (CFRP) was proposed. A set of three-dimensional finite element models of the repaired PCCP have been proposed and implemented in the ABAQUS software, which took into account the soil pressure, the weight of the PCCP, the weight of the water, and the hydrostatic pressure. The stress–strain features of the PCCP repaired with CFRP of various thicknesses were analyzed. The stress–strain features of different wire breakage rates for the repaired PCCP were also analyzed. The results showed that the strains and stresses decreased at the springline if the PCCP was repaired with CFRP, which improved the operation of the PCCP. It has been found that the wire breakage rates had a significant effect on the strains and stresses of each PCCP component, but CFRP failed to reach its potential tensile strength when other materials were broken.

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