Magnetic condensation, Abelian dominance and instability of Savvidy vacuum

We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho--Faddeev--Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconductivity picture of quark confinement. Finally, we discuss the implication to the Faddeev-Skyrme model with knot soliton as a low-energy effective theory of Yang-Mills theory.Comment: 14 pages, 2 figures; a version accepted in Phys. Lett. B, Main changes in sections 2.5 and 2.6. in order to explain the crucial idea bette

The `BRST-invariant' Condensate of Dimension Two in QCD

The status of the `BRST-invariant' condensate of mass dimension two in QCD is explained. The condensate is only invariant under an `on-shell' BRST symmetry which includes a partial gauge-fixing. The on-shell BRST symmetry represents the residual gauge symmetry under gauge transformations which preserve the partial gauge fixing. The gauge-invariant operators which correspond to the BRST-invariant condensate are identified in the Lorentz and maximal Abelian gauges and are shown to be invariant under the residual gauge transformations.Comment: 6 page

Reformulating SU(N) Yang-Mills theory based on change of variables

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement. The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential.Comment: 51 pages, 1 figure; version to be published in Prog. Theor. Phys. Vol. 120, No.1 (2008

Yang-Mills theory constructed from Cho--Faddeev--Niemi decomposition

We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the same local and global gauge symmetries as the original Yang-Mills theory. This may shed new light on the fundamental issue of the discrepancy between two theories for independent degrees of freedom and the role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this consideration gives new insight into the meaning of the gauge invariance and the observables, e.g., a gauge-invariant mass term and vacuum condensates of mass dimension two. We point out the implications for the Skyrme--Faddeev model.Comment: 17pages, 1 figure; English improved; a version appeared in Prog. Theor. Phy

Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement (A review)

This is a brief summary of recent works on the possibility of vacuum condensate of mass dimension 2 in Yang-Mills theory as the gluon sector of QCD. In particular, I discuss the physical implications due to this condensate, especially, for the mass gap and quark confinement. This talk is mainly based on a recent paper [1] and papers in preparation [2].Comment: 13 pages, no figures, Talk presented at the workshop ``Structure and Reaction of Hadrons based on non-perturbative QCD" held at the Research Center of Nuclear Physics (RCNP), Osaka University, Japan, 23-24 July 200

The exact decomposition of gauge variables in lattice Yang-Mills theory

In this paper, we consider lattice versions of the decomposition of the Yang- Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2) and SU(3). As a result, we obtain the general form of the decomposition for SU(N) gauge link variables and confirm the previous results obtained for SU(2) and SU(3).Comment: 16 page

BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition

We determine the nilpotent BRST and anti-BRST transformations for the Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new interpretation given in the previous paper of the Cho--Faddeev-Niemi decomposition. This gives a firm ground for performing the BRST quantization of the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We propose also a modified version of the new Maximal Abelian gauge which could play an important role in the reduction to the original Yang-Mills theory.Comment: 11 pages, no figure; Introduction improved, 3 references adde

Detection of spin voltaic effect in a p-n heterojunction

Model calculation and experimental data of circularly-polarized-light-dependent photocurrent in a n-AlGaAs/p-InGaAs/p-GaAs heterostructure are reported. It is found that, under the appropriate forward bias condition, spin voltaic effect (SVE) can survive across the heterojunction and give rise to detectable polarization-dependent photocurrent signals which are greater than the signals due to the magnetic circular dichroism. Our analysis suggests that SVE can be enhanced by optimization of layer thickness, doping profile, and applied bias, making SVE favorable for the realization of a semiconductor-based polarization detector, a spin-photodiode (spin-PD).Comment: 16 pages, 3figure