Vortices, Infrared effects and Lorentz Invariance Violation

Abstract

The Yang-Mills theory with noncommutative fields is constructed following Hamiltonian and lagrangean methods. This modification of the standard Yang-Mills theory shed light on the confinement mechanism viewed as a Lorentz invariance violation (LIV) effect. The modified Yang-Mills theory contain in addition to the standard contribution, the term ${\theta }^{\mu }{\epsilon }_{\mu \nu \rho \lambda }(A^{\nu }{F}^{\rho \lambda }+2/3A_{\nu }{A}_{\rho }{A}_{\lambda })$ where ${\theta }_{\mu }$ is a given space-like constant vector with canonical dimension of energy. The $A_{\mu }$ field rescaling and the choice ${\theta }_{\mu }=(0,0,0,\theta )$, one can show that the modified Yang-Mills theory in 3+1 dimensions can be made equivalent to a Yang-Mills-Chern-Simons theory in 2+1 dimensions if one consider only heavy fermionic excitations. Thus, the Yang-Mills-Chern-Simons theory in 2+1 dimensions is a codified way of $QCD$ that include only heavy quarks. The classical solutions of the modified Yang-Mills theory for the SU(2) gauge group are confining ones.

Title changed and comments added. To appear in PLB