Stability of the Magnetic Monopole Condensate in three- and four-colour QCD

It is argued that the ground state of three- and four-colour QCD contains a monopole condensate, necessary for the dual Meissner effect to be the mechanism of confinement, and support its stability on the grounds that it gives the off-diagonal gluons an effective mass sufficient to remove the unstable ground state mode.Comment: jhep.cls, typos corrected, references added, some content delete

STATIC FOUR-DIMENSIONAL ABELIAN BLACK HOLES IN KALUZA-KLEIN THEORY

Static, four-dimensional (4-d) black holes (BH's) in ($4+n$)-d Kaluza-Klein (KK) theory with Abelian isometry and diagonal internal metric have at most one electric ($Q$) and one magnetic ($P$) charges, which can either come from the same $U(1)$-gauge field (corresponding to BH's in effective 5-d KK theory) or from different ones (corresponding to BH's with $U(1)_M\times U(1)_E$ isometry of an effective 6-d KK theory). In the latter case, explicit non-extreme solutions have the global space-time of Schwarzschild BH's, finite temperature, and non-zero entropy. In the extreme (supersymmetric) limit the singularity becomes null, the temperature saturates the upper bound $T_H=1/4\pi\sqrt{|QP|}$, and entropy is zero. A class of KK BH's with constrained charge configurations, exhibiting a continuous electric-magnetic duality, are generated by global $SO(n)$ transformations on the above classes of the solutions.Comment: 11 pages, 2 Postscript figures. uses RevTeX and psfig.sty (for figs) paper and figs also at ftp://dept.physics.upenn.edu/pub/Cvetic/UPR-645-

Chromoelectric Knot in QCD

We argue that the Skyrme theory describes the chromomagnetic (not chromoelectric) dynamics of QCD. This shows that the Skyrme theory could more properly be interpreted as an effective theory which is dual to QCD, rather than an effective theory of QCD itself. This leads us to predict the existence of a new type of topological knot, a twisted chromoelectric flux ring, in QCD which is dual to the chromomagnetic Faddeev-Niemi knot in Skyrme theory. We estimate the mass and the decay width of the lightest chromoelectric knot to be around $50 GeV$ and $117 MeV$.Comment: 4 page

Knot Topology of QCD Vacuum

We show that one can express the knot equation of Skyrme theory completely in terms of the vacuum potential of SU(2) QCD, in such a way that the equation is viewed as a generalized Lorentz gauge condition which selects one vacuum for each class of topologically equivalent vacua. From this we show that there are three ways to describe the QCD vacuum (and thus the knot), by a non-linear sigma field, a complex vector field, or by an Abelian gauge potential. This tells that the QCD vacuum can be classified by an Abelian gauge potential with an Abelian Chern-Simon index.Comment: 4 page

Teleparallel Equivalent of Non-Abelian Kaluza-Klein Theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher-dimensional, spacetime being kept always four-dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast to the ordinary Kaluza-Klein models, this theory defines a natural length-scale for the compact sub-manifold of the fiber space, which is shown to be of the order of the Planck length.Comment: Revtex4, 7 pages, no figures, to appear in Phys. Rev.

Thermodynamic and gravitational instability on hyperbolic spaces

We study the properties of anti--de Sitter black holes with a Gauss-Bonnet term for various horizon topologies (k=0, \pm 1) and for various dimensions, with emphasis on the less well understood k=-1 solution. We find that the zero temperature (and zero energy density) extremal states are the local minima of the energy for AdS black holes with hyperbolic event horizons. The hyperbolic AdS black hole may be stable thermodynamically if the background is defined by an extremal solution and the extremal entropy is non-negative. We also investigate the gravitational stability of AdS spacetimes of dimensions D>4 against linear perturbations and find that the extremal states are still the local minima of the energy. For a spherically symmetric AdS black hole solution, the gravitational potential is positive and bounded, with or without the Gauss-Bonnet type corrections, while, when k=-1, a small Gauss-Bonnet coupling, namely, \alpha << {l}^2 (where l is the curvature radius of AdS space), is found useful to keep the potential bounded from below, as required for stability of the extremal background.Comment: Shortened to match published (PRD) version, 18 pages, several eps figure

The Effective Energy-Momentum Tensor in Kaluza-Klein Gravity With Large Extra Dimensions and Off-Diagonal Metrics

We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. In addition, we find two four-vectors, J_{m}^{mu} and J_{e}^{mu}, induced by off-diagonal metrics, that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor {F-hat}_{mu nu} that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the dimensional reduction. Thus, if {F-hat}_{mu nu} could be identified with the electromagnetic tensor, then the theory would predict the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent on how we choose our space-time coordinates from those of the bulk.Comment: New title, editorial changes made as to match the version to appear in International Journal of Modern Physics

Decomposition of meron configuration of SU(2) gauge field

For the meron configuration of the SU(2) gauge field in the four dimensional Minkowskii spacetime, the decomposition into an isovector field \bn, isoscalar fields $\rho$ and $\sigma$, and a U(1) gauge field $C_{\mu}$ is attained by solving the consistency condition for \bn. The resulting \bn turns out to possess two singular points, behave like a monopole-antimonopole pair and reduce to the conventional hedgehog in a special case. The $C_{\mu}$ field also possesses singular points, while $\rho$ and $\sigma$ are regular everywhere.Comment: 18 pages, 5 figures, Sec.4 rewritten. 5 refs. adde

Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory

We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the noncommutativity scale. The effective field theory can also contain higher-curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.Comment: 31 pages LaTeX; References adde

Illusions of general relativity in Brans-Dicke gravity

Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity when omega tends to infinity is false if the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.Comment: 16 pages, LaTeX, to appear in Physical Review