CONFINEMENT EFFECT AS A RESULT OF SPONTANEOUS BREAKING OF SCALE INVARIANCE

In this paper the consequences of introducing spontaneous symmetry breaking of scale invariance through a scale that is obtained from the integration of the equations of motion of four index field strengths are studied. Confinement is obtained for all values of this constant of integration. For negative values two point charges have a potential energy that grows linearly with distance, but they can be arbitrarily far apart (although this is costly from the point of view of energy). For positive values of the integration constant, there is no possibility of separating charges too far apart; at a certain point a new charge of opposite sign has to be added to form a neutral system that cannot be bigger that a critical size. We discuss this using different methods, including some developed by Adler and Piran. In addition, we discuss a few alternative effective actions that are similar and that also give confinement.

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BAGS AND CONFINEMENT GOVERNED BY SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

International Journal of Modern Physics A ◽

10.1142/s0217751x10050305 ◽

2010 ◽

Vol 25 (22) ◽

pp. 4195-4220 ◽

Cited By ~ 12

Author(s):

E. I. GUENDELMAN

Keyword(s):

Energy Density ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Gauge Field ◽

Scale Invariance ◽

Vacuum Energy ◽

Equations Of Motion ◽

Flat Space ◽

Vacuum Energy Density ◽

Conformally Invariant

A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard [Formula: see text] where g is the determinant of the metric and another measure Φ independent of the metric. To implement scale invariance, a dilaton field is introduced. Using the first-order formalism, curvature (ΦR and [Formula: see text]) terms, gauge field term ([Formula: see text] and [Formula: see text]) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well-defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is nonconfining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.

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Gauge hierarchies for chiral SU(N) × SU(N) groups

Canadian Journal of Physics ◽

10.1139/p76-196 ◽

1976 ◽

Vol 54 (16) ◽

pp. 1660-1663 ◽

Cited By ~ 1

Author(s):

Shalom Eliezer

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Gauge Theories ◽

Vacuum Expectation ◽

Coupling Constants ◽

Spontaneous Breaking ◽

Text Representation ◽

Algebraic Equations ◽

Expectation Values ◽

Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

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Spontaneous Symmetry Breaking in 5D Conformally Invariant Gravity

Advances in High Energy Physics ◽

10.1155/2016/5353267 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Taeyoon Moon ◽

Phillial Oh

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Conformal Symmetry ◽

Brane World ◽

Spontaneous Breaking ◽

Warp Factor ◽

Translational Symmetry ◽

Tensor Perturbation ◽

Conformally Invariant ◽

Conformal Quantum Mechanics

We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implements the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting system is described by the conformal quantum mechanics. Possible applications to the spontaneous symmetry breaking of time-translational symmetry along the dynamical fifth direction and the brane-world scenario are discussed.

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Chiral Symmetry

Concepts of Elementary Particle Physics ◽

10.1093/oso/9780198812180.003.0014 ◽

2019 ◽

pp. 217-230

Author(s):

Michael E. Peskin

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Chiral Symmetry ◽

Goldstone Boson ◽

Spontaneous Breaking ◽

Quark Masses ◽

Zero Mass ◽

K Mesons ◽

The Masses

This chapter introduces chiral symmetry, the extra symmetry that QCD acquires when the masses of quarks are set to zero. It introduces the concept of spontaneous symmetry breaking and explains the spontaneous breaking of chiral symmetry in QCD. It introduces the concept of a Goldstone boson, a particle that has zero mass as the result of spontaneous symmetry breaking, and explains how this concept explains properties of the pi and K mesons and allows us to determine the underlying values of the quark masses.

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STRONG INTERACTION DYNAMICS FROM SPONTANEOUS SYMMETRY BREAKING OF SCALE INVARIANCE

Modern Physics Letters A ◽

10.1142/s0217732307023638 ◽

2007 ◽

Vol 22 (17) ◽

pp. 1209-1215 ◽

Cited By ~ 15

Author(s):

E. I. GUENDELMAN

Keyword(s):

High Temperature ◽

Simple Model ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Strong Interaction ◽

Scale Invariance ◽

Maximal Rank ◽

Dilaton Field ◽

Interaction Dynamics ◽

Temperature Dynamics

Using the mechanism of spontaneous symmetry breaking of scale invariance obtained from the dynamics of maximal rank field strengths, it is possible to spontaneously generate confining behavior. Introducing a dilaton field, the study of nontrivial confining and de-confining transitions appears possible. This is manifest in two ways at least: One can consider bags which contain an unconfined phase in the internal region and a confined phase outside and also one obtains a simple model for deconfinement at high temperature from the finite temperature dynamics of the dilaton field.

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A semiclassical approach for the Higgs boson

International Journal of Modern Physics A ◽

10.1142/s0217751x14501966 ◽

2014 ◽

Vol 29 (32) ◽

pp. 1450196

Author(s):

Amir H. Fariborz ◽

Renata Jora ◽

Joseph Schechter

Keyword(s):

Higgs Boson ◽

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Equations Of Motion ◽

Tree Level ◽

Semiclassical Approach ◽

Gauge Bosons ◽

The Masses ◽

Simple Tree

Starting from the equations of motion of the fields in a theory with spontaneous symmetry breaking and by making some simple assumptions regarding their behavior we derive simple tree level relations between the mass of the Higgs boson in the theory and the masses of the gauge bosons corresponding to the broken generators. We show that these mass relations have a clear meaning if both the scalars and the gauge bosons in the theory are composite states made of two fermions.

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