Vortices, Infrared effects and Lorentz Invariance Violation

TL;DR

This paper constructs a modified noncommutative Yang-Mills theory that incorporates Lorentz invariance violation effects, revealing connections to confinement mechanisms and lower-dimensional Chern-Simons theories.

Contribution

It introduces a noncommutative extension of Yang-Mills theory with LIV terms, linking 3+1D confinement to 2+1D Yang-Mills-Chern-Simons models for heavy quarks.

Findings

Classical solutions are confining for SU(2) gauge group.

Modified theory is equivalent to a 2+1D Yang-Mills-Chern-Simons theory under certain conditions.

The LIV term provides insight into confinement mechanisms.

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 $\theta^\mu \epsilon_{\mu \nu \rho \lambda} (A^\nu F^{\rho \lambda} + {2/3} A_\nu A_\rho A_\lambda)$ 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.