A gauge invariant infrared stabilization of 3D Yang-Mills gauge theories

Abstract

We demonstrate that the inversion method can be a very useful tool in providing an infrared stabilization of 3D gauge theories, in combination with the mass operator $A^2$ in the Landau gauge. The numerical results will be unambiguous, since the corresponding theory is ultraviolet finite in dimensional regularization, making a renormalization scale or scheme obsolete. The proposed framework is argued to be gauge invariant, by showing that the nonlocal gauge invariant operator $A_{\min }^2$, which reduces to $A^2$ in the Landau gauge, could be treated in 3D, in the sense that it is power counting renormalizable in any gauge. As a corollary of our analysis, we are able to identify a whole set of powercounting renormalizable nonlocal operators of dimension two.

arXiv comment16 pages, 14 figures. v2: version to appear in JPhysA

References in corpus (23)

• SU(N) gauge theories in 2+1 dimensions
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Constituent Quarks from QCD
• The non-perturbative groundstate of Q.C.D and the local composite operator A_mu^2
• Phase Structure and Phase Transition of the SU(2) Higgs Model in Three Dimensions
• Positivity violation for the lattice Landau gluon propagator
• The anomalous dimension of the composite operator A^2 in the Landau gauge
• A Self-consistent Inclusion of Magnetic Screening for the Quark-Gluon Plasma
• Three loop MSbar renormalization of the Curci-Ferrari model and the dimension two BRST invariant composite operator in QCD
• SU(2) Landau gluon propagator on a 140^3 lattice
• Feynman Diagrams to Three Loops in Three Dimensional Field Theory
• Seeking an Even-Parity Mass Term for 3-D Gauge Theory
• Threshhold Singularities and the Magnetic Mass in Hot QCD
• Renormalizability of the local composite operator A^2 in linear covariant 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
• The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory
• Gauge invariance and mass gap in (2+1)-dimensional Yang-Mills theory
• Quantum properties of a non-Abelian gauge invariant action with a mass parameter
• Renormalization properties of the mass operator A^2 in three dimensional Yang-Mills theories in the Landau gauge
• UV finiteness of 3D Yang-Mills theories with a regulating mass in the Landau gauge
• One loop renormalization of the non-local gauge invariant operator min_U (A^U_mu)^2 in QCD
• Renormalizability of the dimension two gluon operator $A^2$ in a class of nonlinear covariant gauges