<A^2> Condensate, Bianchi Identities and Chromomagnetic Fields Degeneracy in SU(2) YM Theory

Abstract

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 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 to study the problem numerically. We present evidences 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 non-trivial sector. However, confronting the results obtained in three and four dimensions we argue that it is the mass dimension two condensate <A^2_{min}> which probably explains our findings.

21 pages, 17 EPS figures, revtex4; added references, typos corrected; replaced to match the published version (PRD, to appear)

References in corpus (5)

• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• The Dual Meissner Effect and Magnetic Displacement Currents
• Lower-dimension vacuum defects in lattice Yang-Mills theory
• Interpreting the lattice monopoles in the continuum terms
• Hints on dual variables from the lattice SU(2) gluodynamics

Cited by in corpus (14)

• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges
• A study of the gauge invariant, nonlocal mass operator $Tr\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in Yang-Mills theories
• A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges
• Quantum properties of a non-Abelian gauge invariant action with a mass parameter
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• A combined study of the gluon and ghost condensates <A^2> and <epsilon^{abc} cbar^b c^c> in Euclidean SU(2) Yang-Mills theory in the Landau gauge
• The asymmetry of the dimension 2 gluon condensate: the zero temperature case
• A two-component picture of the <A^2> condensate with instantons
• The asymmetry of the dimension 2 gluon condensate: the finite temperature case
• Renormalizability of pure $\mathcal{N}=1$ Super Yang-Mills in the Wess-Zumino gauge in the presence of the local composite operators $A^2$ and $\bar{\lambda }\lambda$
• Non-perturbative aspects of Yang-Mills theories
• Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
• Covariant Mass and Geometrical setup in Euclidean gauge theories