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We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen (SNO) effective action.

We consider Weyl symmetric structure of the classical vacuum in quantum chromodynamics. In the framework of formalism of gauge invariant Abelian projection we show that classical vacuums can be constructed in terms of Killing vector fields on the group SU(3). Consequently, homotopic classes of Killing vector fields determine the topological structure of the vacuum. In particular, the second homotopy group \pi_2(SU(3)/U(1)\times U(1)) describes all topologically non-equivalent vacuums which are classified by two topological numbers. For each given Killing vector field one can construct six vacuums forming Weyl sextet representation. An interesting feature of SU(3) gauge theory is that it admits a Weyl symmetric vacuum represented by a linear superposition of the six vacuums from the Weyl vacuum sextet. A non-trivial manifestation of Weyl symmetry is demonstrated on monopole solutions. We construct a family of finite energy monopole solutions in Yang-Mills-Higgs theory which includes Weyl monopole sextet. From the analysis of the classical vacuum structure and monopole solutions we conjecture that a similar Weyl symmetric vacuum structure can be realized in quantum theory., Comment: 13 pages

We present finite energy analytic monopole and dyon solutions whose size is fixed by the electroweak scale. Our result shows that genuine electroweak monopole whose mass is around 6.7 TeV could exist, which could be detected at LHC., Comment: 4 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:hep-th/9705213

We investigate the relationship between colour confinement and the monopoles derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and 't Hooft monopoles, do not require a singular gauge field and are defined for any choice of gauge (and are not just restricted to, for example, the maximum Abelian gauge). The Abelian decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to investigate the relationship between the gauge invariant monopoles and confinement both analytically and numerically, as well as retaining the maximal possible symmetry within the colour field so that it is able to see all the monopoles in an SU($N_C$) calculation. We describe how the Abelian decomposition is related to the Wilson Loop, so that the string tension may be calculated from the field strength related to the decomposed (or restricted) Abelian field. We discuss the structures in the colour field which may cause an area law in the Wilson Loop, which turn out to be magnetic monopoles. If these monopoles are present, they will lead to an area law scaling of the Wilson Loop and thus be at least partially responsible for confinement. We search for these monopoles in quenched lattice QCD. We show that the string tension is dominated by peaks in the restricted field strength, at least some of which are located close to structures in the colour field consistent with with theoretical expectations for the monopoles. We show that the string tension extracted from the monopole contribution to the restricted field is close to that of the entire original field; again suggesting that confinement can at least partially be explained in terms of these monopoles., Comment: Lattice 2012 (Chiral Symmetry), 7 pages

Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) $\vGm_\mu$ into the restricted connection made of the potential of the maximal Abelian subgroup $H$ of Lorentz group $G$ and the valence connection made of $G/H$ part of the potential which transforms covariantly under Lorentz gauge transformation. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, the light-like (or null) decomposition and the non light-like (or non-null) decomposition, because Lorentz group has two maximal Abelian subgroups. In this decomposition the role of the metric $g_\mn$ is replaced by a four-index metric tensor $\vg_\mn$ which transforms covariantly under the Lorentz group, and the metric-compatibility condition $\nabla_\alpha g_\mn=0$ of the connection is replaced by the gauge and generally covariant condition ${\mathscr D}_\mu \vg^\mn=0$. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler and has less physical degrees of freedom than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-one field.

~Based on the gauge invariant quark canonical momentum we construct two theoretically possible decompositions of nucleon momentum to those of quarks and gluons. We predict that either 6% or 21% of nucleon momentum is carried by gluons, depending on what type of gluons are in nucleons. We clarify the existing confusions on this problem and discuss the physical implications of our result on the proton spin crisis problem.

We discuss the shortfalls of existing resolutions of the long-standing gauge invariance problem of the canonical decomposition of the nucleon spin to the spin and angular momentum of quarks and gluons. We provide two logically flawless expressions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all gluons (binding and valence gluons) contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it. We propose the second expression to be the physically correct one.

Assuming that the dilaton is the dark matter of the universe, we propose an experiment to detect the relic dilaton using the electromagnetic resonant cavity, based on the dilaton-photon conversion in strong electromagnetic background. We calculate the density of the relic dilaton, and estimate the dilaton mass for which the dilaton becomes the dark matter of the universe. With this we calculate the dilaton detection power in the resonant cavity, and compare it with the axion detection power in similar resonant cavity experiment., Comment: 23 pages, 2 figures

Based on the fact that the scalar curvature of the internal space determines the mass of the dilaton in higher-dimensional unified theories, we show how the dilaton mass can explain the origin of mass and resolve the hierarchy problem. Moreover, we show that cosmology puts a strong constraint on dilaton mass, and requires the scale of the internal space to be larger than $10^{-9} m$., Comment: 5 pages, 1 figure

We consider one-loop effective action of SU(3) QCD with a most general constant chromomagnetic (chromoelectric) background which has two independent Abelian field components. The effective potential with a pure magnetic background has a local minimum only when two Abelian components H_{\mu\nu}^3 and H_{\mu\nu}^8 of color magnetic field are orthogonal to each other. The non-trivial structure of the effective action has important implication in estimating quark-gluon production rate and p_T-distribution in quark-gluon plasma. In general the production rate depends on three independent Casimir invariants, in particular, it depends on the relative orientation between chromoelectric fields., Comment: 6 pages, 3 figures (9 pages in published version)

The effects of light propagation in constant magnetic and electric backgrounds are considered in the framework of the effective action approach. We use the exact analytic series representation for the one-loop effective action of QED and apply it to the birefringence effect. Analytical results for the light velocity modes are obtained for weak and strong field regime. We present asymptotic formulae for the light velocity modes for the ultra strong magnetic field which can be realized in some neutron stars., Comment: 9 pages, 4 figs, accepted by Phys. Rev. D