Hints of confinement and deconfinement in Yang-Mills-Chern-Simons theories in the maximal Abelian gauge

Infrared propagators of Yang-Mills-Chern-Simons theories in linear covariant gauges

“…Since the gauge condition can be taken as Landau gauge ∂ µ A a µ = 0, all the discussion made before regarding the existence and treatment of infinitesimal Gribov copies can be simply imported to the case of YMCS theories. This was investigated in [39,40] in the Landau gauge and in [41] in the maximal Abelian gauge. As a difference with respect to pure Yang-Mills theories, the topological mass M enters the gap equation that fixes the Gribov parameter as observed in [41].…”

“…This was investigated in [39,40] in the Landau gauge and in [41] in the maximal Abelian gauge. As a difference with respect to pure Yang-Mills theories, the topological mass M enters the gap equation that fixes the Gribov parameter as observed in [41]. See also [42].…”

“…( 13) that M enters as a mass parameter in the gaugefield propagator. As it was investigated in [39][40][41][42], the presence of the Gribov parameter γ in the gauge-field propagator has a non-trivial interference with M , which changes the pole-structure of the gauge-field propagator and the interpretation of (non-)physical excitations in the spectrum of the theory. The paper is organized as follows: In Sect.…”

Implications of the Topological Chern-Simons mass in the Gap Equation

“…In 44 years, a big range of research has been done based in the Gribov problem, for curiosity the reader can see [2][3][4][5][6][7][8]. The pioneer work was done by Zwanziger, who figured out how to implement the Gribov region in the action, hence developing a new formalism called Gribov-Zwanziger formalism [9][10][11], what some authors have used to understand and explain confinement/deconfinement phase transition, see some example here [12][13][14][15].…”

“…Another very interesting method to study confinement/deconfinement is through 3d Euclidean Yang-Mills-Chern-Simons theory [16,17], because the topological Chern-Simons (CS) mass term gives the gluon field an extra mass generating a confinement/deconfinement transition phase [12,13] in 3d Euclidean Yang-Mills. Now, it sounds much more interesting if we join Gribov-Zwanziger formalism and Yang-Mills-Chern-Simons theory and analyze what happens with the gap equation (the equation that defines the Gribov horizon [1,[9][10][11]) and with the gluon propagator poles in the presence of a topological mass and the Gribov parameter γ 4 .…”