Axially symmetric, static self-dual Yang-Mills and stationary Einstein-gauge field equations

1984 ◽  
Vol 30 (2) ◽  
pp. 486-488 ◽  
Author(s):  
Metin Gürses
Keyword(s):  
Gauge Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Yang Mills

APPROXIMATE SOLUTIONS OF STATIONARY GAUGE STRINGS ON THE (r, z)-PLANE

1995 ◽  
Vol 04 (02) ◽  
pp. 267-277 ◽  
Author(s):  
R.J. SLAGTER
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Approximation Scheme ◽  
Analytic Solution ◽  
Approximate Solutions ◽  
Second Order ◽  
Singular Behavior ◽  
Axially Symmetric ◽  
Field Equations ◽  
Symmetric Spacetime

We derive a class of approximate solutions of the coupled Einstein-scalar-gauge field equations on an axially symmetric spacetime. An analytic solution of the resulting elliptic PDE’s can be obtained to any desired order by constructing the Riemann functions. As an example model, a solution is presented, which resembles the Nielsen-Olesen vortex close to the z=0 hyperplane. However, the solution shows some significant deviation from the classical vortex off the z=0 plane. The singular behavior, which one usually encounters in line-mass models, manifests itself through the second-order solutions in the approximation scheme. Further, in this “toy”-model, with sufficient angular momentum of the spinning string, gφφ becomes negative for some values of r.

scholarly journals GRAVITY-ASSISTED SOLUTION OF THE MASS GAP PROBLEM FOR PURE YANG–MILLS FIELDS

2011 ◽  
Vol 08 (06) ◽  
pp. 1355-1418 ◽  
Author(s):  
ARKADY L. KHOLODENKO
Keyword(s):  
Symmetry Transformation ◽  
Nucl Phys ◽  
Strong Interactions ◽  
Axially Symmetric ◽  
Field Equations ◽  
Yang Mills ◽  
Heterotic Strings ◽  
Ernst Equation ◽  
Mass Gap ◽  
Pure Gravity

In 1979, Louis Witten demonstrated that stationary axially symmetric Einstein field equations and those for static axially symmetric self-dual SU (2) gauge fields can both be reduced to the same (Ernst) equation. In this paper, we use this result as point of departure to prove the existence of the mass gap for quantum source-free Yang–Mills (Y–M) fields. The proof is facilitated by results of our recently published paper, J. Geom. Phys.59 (2009) 600–619. Since both pure gravity, the Einstein–Maxwell and pure Y–M fields are described for axially symmetric configurations by the Ernst equation classically, their quantum descriptions are likely to be interrelated. Correctness of this conjecture is successfully checked by reproducing (by different methods) results of Korotkin and Nicolai, Nucl. Phys. B475 (1996) 397–439, on dimensionally reduced quantum gravity. Consequently, numerous new results supporting the Faddeev–Skyrme (F–S)-type models are obtained. We found that the F–S-like model is best suited for description of electroweak interactions while strong interactions require extension of Witten's results to the SU(3) gauge group. Such an extension is nontrivial. It is linked with the symmetry group SU (3) × SU (2) × U (1) of the standard model. This result is quite rigid and should be taken into account in development of all grand unified theories. Also, the alternative (to the F–S-like) model emerges as by-product of such an extension. Both models are related to each other via known symmetry transformation. Both models possess gap in their excitation spectrum and are capable of producing knotted/linked configurations of gauge/gravity fields. In addition, the paper discusses relevance of the obtained results to heterotic strings and to scattering processes involving topology change. It ends with discussion about usefulness of this information for searches of Higgs boson.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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