We show how to generalize the previous result of the monopole condensation in SU(2) QCD to SU(3) QCD. We present the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and
the colored chromons. The decomposition allows us to separate the gauge invariant and parity conserving monopole background gauge independently, and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry which is easier to handle. With this we obtain the infra-red finite and gauge invariant integral expression of the one-loop effective action which is Weyl symmetric in three SU(2) subgroups. Integrating it gauge invariantly imposing the color reflection invariance we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result.
The recent MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss different ways to estimate the mass of the electroweak monopole. We first present a scaling argum
ent which indicates that the mass of the electroweak monopole to be around 4 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strengths of the electromagnetic interaction of $W$-boson in the standard model. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC.
Viewing Einsteins theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology $pi_3(S^3)simeq pi_3(S^2)
$ of $pi_3(SO(3,1))$. With this we obtain the gauge independent vacuum decomposition of Einsteins theory to the vacuum and gauge covariant physical parts. We discuss the physical implications of our result in quantum gravity.
