On Gribov's supercriticality picture of quark confinement

Some years ago Gribov developed the so-called supercritical light-quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson-Schwinger equation in the complex plane and discuss new characteristics of dynamical chiral symmetry breaking in our truncation scheme. (orig.)