Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism

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Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for hig (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as scaling features an infrared power law for the gluon and ghost propagators, the massive solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the massive-type solutions minimize the quantum effective action.
© 2012 American Physical Society. We wish to thank D. Zwanziger for his continued support and contributions to this work. We also thank R. Alkofer, C. Fischer and L. von Smekal for discussions and a critical reading of this manuscript. This work has been supported by Grants No. FPA2011-27853-01, No. FIS2008-01323 (Spain) and by the Austrian Science Fund FWF under Project No. M1333-N16.
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