⟨A2⟩ condensate, Bianchi identities, and chromomagnetic field degeneracy in SU(2) Yang-Mills theory -: art. no. 114514

We consider the non-Abelian Bianchi identities in SU(2) pure Yang-Mills theory in D=3,4 focusing on the possibility of their violation and the significance of the chromomagnetic fields degeneracy points. We show that the recently proposed non-Abelian Stokes theorem allows one to formulate the Bianchi identities in terms of the physical fluxes and their relative color orientations. Then the violation of Bianchi identities becomes a well defined concept ultimately related to the degeneracy points. The locality and gauge invariance of our approach allows one to study the problem numerically. We present evidence that in D=4 the suppression of the Bianchi identities violation is likely to destroy confinement, while the removal of the degeneracy points drives the theory to the topologically nontrivial sector. However, confronting the results obtained in three and four dimensions, we argue that it is the mass dimension two condensate < A(min)(2)> which probably explains our findings.