scholarly journals Influence of Fermions on Vortices in SU(2)-QCD

2021 ◽  
Author(s):  
Zeinab Dehghan ◽  
Sedigheh Deldar ◽  
Manfried Faber ◽  
Rudolf Golubich ◽  
Roman Höllwieser
Keyword(s):  
Gauge Field ◽  
String Tension ◽  
Gauge Fields ◽  
Back Reaction ◽  
Vortex Model ◽  
Full Theory ◽  
Qcd Vacuum ◽  
Center Vortex ◽  
Fermionic Fields

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields.

scholarly journals Influence of Fermions on Vortices in SU(2)-QCD

2019 ◽  
Author(s):  
Nikita Astrakhantsev ◽  
Manfried Faber ◽  
Rudolf Golubich ◽  
Andrey Kotov ◽  
Aleksandr Nikolaev
Keyword(s):  
Gauge Field ◽  
The Other ◽  
Gauge Fields ◽  
Back Reaction ◽  
Qcd Vacuum ◽  
Other Hand

Gauge fields control the dynamics of fermions. On the other hand a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum.

scholarly journals Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

Particles ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 491-498 ◽  
Author(s):  
Rudolf Golubich ◽  
Manfried Faber
Keyword(s):  
Simulated Annealing ◽  
Magnetic Flux ◽  
Degrees Of Freedom ◽  
Chiral Symmetry Breaking ◽  
String Tension ◽  
Local Maxima ◽  
Vortex Model ◽  
Center Vortex ◽  
Nontrivial Center ◽  
Vortex Detection

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions—that is, regions whose boundary evaluates to a nontrivial center element—a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

scholarly journals GINZBURG–LANDAU EQUATION FROM SU(2) GAUGE FIELD THEORY

2003 ◽  
Vol 18 (14) ◽  
pp. 955-965 ◽  
Author(s):  
VLADIMIR DZHUNUSHALIEV ◽  
DOUGLAS SINGLETON
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Landau Equation ◽  
Mass Term ◽  
Gauge Fields ◽  
Electromagnetic Potential ◽  
Complex Scalar ◽  
Ginzburg Landau ◽  
Qcd Vacuum ◽  
Complex Scalar Field

The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

scholarly journals Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

2019 ◽  
Author(s):  
Rudolf Golubich ◽  
Manfried Faber
Keyword(s):  
Simulated Annealing ◽  
Magnetic Flux ◽  
Degrees Of Freedom ◽  
Chiral Symmetry Breaking ◽  
String Tension ◽  
Local Maxima ◽  
Vortex Model ◽  
Center Vortex ◽  
Trivial Center ◽  
Vortex Detection

The center vortex model of quantum chromodynamic states that vortices, closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using non-trivial center regions, that is, regions whose boundary evaluates to a non-trivial center element, a resolution of this issue seems possible. We use such non-trivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

scholarly journals A Possible Resolution to Troubles of SU(2) Center Vortex Detection in Smooth Lattice Configurations

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 122
Author(s):  
Rudolf Golubich ◽  
Manfried Faber
Keyword(s):  
Symmetry Breaking ◽  
Quantum Chromodynamics ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Vortex Model ◽  
Center Vortex ◽  
Vortex Detection

The center vortex model of quantum-chromodynamics can explain confinement and chiral symmetry breaking. We present a possible resolution for problems of the vortex detection in smooth configurations and discuss improvements for the detection of center vortices.

scholarly journals Gauge field back reaction on a black hole

1993 ◽  
Vol 47 (4) ◽  
pp. 1465-1470 ◽  
Author(s):  
David Hochberg ◽  
Thomas W. Kephart
Keyword(s):  
Black Hole ◽  
Gauge Field ◽  
Back Reaction

scholarly journals Vertex Corrections in Gauge Theories for Two-dimensional Condensed Matter Systems

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1673-1692 ◽  
Author(s):  
Peter Kopietz
Keyword(s):  
Gauge Field ◽  
Condensed Matter ◽  
Finite Energy ◽  
Energy Scale ◽  
Gauge Fields ◽  
Logarithmic Correction ◽  
Two Dimensional ◽  
Numerical Constant ◽  
Self Energy ◽  
Vertex Corrections

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1/qη, 1<η≤ 2, the fermionic self-energy without vertex corrections vanishes for small frequencies ω as Σ(ω)∝ ωγ with γ=2/(1+η)<1. We show that inclusion of the leading radiative correction to the fermion-gauge field vertex leads to Σ(ω)∝ωγ [1-aη ln (ω0/ω)], where aη is a positive numerical constant and ω0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent γ to larger values.

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