Classical solutions of Yang-Mills and CP n−1 models with scalar fields

1980 ◽  
Vol 6 (3) ◽  
pp. 223-234 ◽  
Author(s):  
Alfred Actor
Keyword(s):  
Scalar Fields ◽  
Classical Solutions ◽  
Yang Mills

THE CONFINEMENT MECHANISM IN YANG–MILLS THEORY?

1999 ◽  
Vol 14 (06) ◽  
pp. 447-457 ◽  
Author(s):  
JOSE A. MAGPANTAY
Keyword(s):  
Gluon Propagator ◽  
Statistical Treatment ◽  
Gauge Condition ◽  
Classical Solutions ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Effective Dynamics ◽  
Gauge Fixing ◽  
Parallel Surfaces ◽  
Nonlinear Gauge

Using the recently proposed nonlinear gauge condition [Formula: see text] we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · Aa=fa≠0. In this sector, the gauge field [Formula: see text] can be expressed in terms of fa and a new vector field [Formula: see text]. The effective dynamics of fa suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) fa(x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · Aa=fa(x) surfaces.

Classical and Semi-Classical Solutions of the Yang-Mills Theory

1978 ◽  
pp. 199-258 ◽  
Author(s):  
R. Jackiw ◽  
C. Nohl ◽  
C. Rebbi
Keyword(s):  
Classical Solutions ◽  
Yang Mills

scholarly journals More about the instanton/soliton/kink correspondence

2016 ◽  
Vol 14 (01) ◽  
pp. 1750012 ◽  
Author(s):  
Andrea Addazi
Keyword(s):  
Soliton Solutions ◽  
Scalar Fields ◽  
Space Time ◽  
Yang Mills ◽  
Charge Formula

We demonstrate that all gauge instantons in a [Formula: see text] Yang–Mills theory, with generic topological vacuum charge [Formula: see text], correspond to soliton solutions and kink scalar fields in [Formula: see text] space-time.

scholarly journals Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Yasuhiro Sekino
Keyword(s):  
Gauge Theory ◽  
Free Field ◽  
Scalar Fields ◽  
Superstring Theory ◽  
Spatial Direction ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Brane Solution ◽  
Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

Classical solutions ofSU(2)Yang—Mills theories

1979 ◽  
Vol 51 (3) ◽  
pp. 461-525 ◽  
Author(s):  
Alfred Actor
Keyword(s):  
Classical Solutions ◽  
Yang Mills

scholarly journals Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Indrajit Mitra ◽  
H. S. Sharatchandra
Keyword(s):  
Boundary Condition ◽  
Gauge Transformation ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Gauge Potential ◽  
Conformally Flat ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Conformally Flat Metrics

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically nontrivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.

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