A first look at Landau-gauge propagators in G₂Yang-Mills theory

Abstract

G 2 Yang-Mills theory is an interesting laboratory to investigate nonperturbative effects. On one hand, no conventional quark confinement via a linearly rising potential is present. On the other hand, its thermodynamic properties are similar to ordinary SU(N ) Yang-Mills theory. Finally, it has been conjectured that gluons are removed from the physical spectrum in the same way as in SU(N ) Yang-Mills theory. The last claim will be explored by determining the Landau-gauge ghost and gluon propagators, as well as the Faddeev-Popov operator eigenspectrum, in G 2 lattice gauge theory in two and three dimensions. The results are found to agree qualitatively with the SU(2) and SU(3) case. Therefore, the conjecture that Yang-Mills theories with different gauge groups are qualitatively similar on the level of their Landau gauge Green's functions is supported.

Gauge bosons at zero and finite temperature

“…The bottom panels show the same, but for gauge algebras su(3-6) and g 2 in MLG [175]. Further lattice results can be found in [91,95,117,118,122,135,253] The situation for the maxB gauge is drastically different [84]. In this case, the ghost propagator is much more divergent than even the scaling case, and more divergent than the results in any of the other gauges.…”

“…The bottom panels show the same, but for gauge algebras su(3-6) and g 2 in MLG [175]. Further lattice results can be found in [91,95,117,118,123,135,251,[253][254][255].…”

Phase diagram of the latticeG2Higgs model

“…The smallest simple and simply connected Lie group with a trivial center is the 14 dimensional exceptional Lie group G 2 . This is one reason why G 2 gauge theory with and without Higgsfields has been investigated in series of papers [6][7][8][9][10][11]. Although there is no symmetry * bjoern.wellegehausen@uni-jena.de, wipf@tpi.uni-jena.de and Christian.Wozar@uni-jena.de reason for a deconfinement phase transition in G 2 gluodynamics it has been conjectured that a first order deconfinement transition without order parameter exists.…”

Topology and θ dependence in finite temperature G 2 lattice gauge theory

“…Bearing all this in mind, it is not surprising that the G 2 lattice gauge theory was actively investigated in the past, both at zero and finite temperature [11][12][13][14][15][16][17][18][19][20][21][22]. What is probably surprising is that the results of these analysis gave a picture much similar to that of standard SU(N ) theory: the spectrum of the G 2 theory at zero temperature is composed only of color neutral objects [11,12,15], the string tension at intermediate distances (i.e.…”

“…What is probably surprising is that the results of these analysis gave a picture much similar to that of standard SU(N ) theory: the spectrum of the G 2 theory at zero temperature is composed only of color neutral objects [11,12,15], the string tension at intermediate distances (i.e. before string breaking [20]) satisfies Casimir scaling [13,18,20], a first order deconfinement transition is present [14,16,22], (quenched) chiral symmetry is broken in the low temperature phase and restored above the critical temperature [19], the topological susceptibility is suppressed above deconfinement [21], propagators [17] and thermodynamical observables (like e.g. pressure and trace anomaly) [22] do not show any qualitative difference with respect to the SU(N ) case.…”