FG 465: Gitter-Hadronen-Phänomenologie - Teilprojekt 2: Confinement, gluon- and ghost propagators and the topological structure of lattice QCD in the vacum and at finite temperature

Our contribution to the Forschergruppe FOR 465 has two major goals. i) We plan to continue the thorough investigation of the topological structure of lattice QCD with special emphasis on carriers of topological charge with non-trivial holonomy (known as Kraan-van Baal solutions). We are attempting to prove numerically the conjecture that quantum gauge fields at non-zero temperature have an underlying semiclassical topological structure in terms of calorons, with BPS monopoles as constituents becoming manifest at the transition to the confinement phase. In the confinement phase, even if not fully accessible to a semiclassical description, fractional lumps of topological charge should be found. The evidence should be presented first for pure SU(3) gauge theory, by identifying the respective structures in Monte Carlo ensembles. Full QCD (with two Wilson fermion flavours) will be explored next. For this purpose various techniques, on one hand bosonic ones like smearing, improved operators of field strength and topological density, gauge fixing to various Abelian gauges, and on the other hand fermionic ones by considering the low-lying fermionic modes of chirally improved fermions will be applied. The topological structure at zero temperature is much more controversial. It is claimed to be determined by instantons, fractional charge instanton constituents, one-dimensional, two- or higher-dimensional extended structures. With the development of appropriate tools (based on overlap fermions) in conjunction with the above-mentioned bosonic methods we hope to contribute to the clarification of this issue. ii) The second line of research considers the confinement problem from the Gribov-Zwanziger viewpoint, i.e. focusing at the singular behaviour of the ghost propagator in the Landau and Coulomb gauge, in the infrared limit. Our aim is to simultaneously compute the gluon and ghost propagators for large lattice sizes under well-defined gauge-fixing prescriptions, first for pure SU(2) and SU(3) gauge theories and then for full lattice QCD, at zero and non-zero temperature. Part of these activities will be the search for better methods to control the Gribov problem in the gauge fixing context and to explore alternative algorithms. A by-product of these studies will be the running coupling alpha_s(q) in a momentum-subtraction scheme. A major task will be to identify confining gauge field excitations putting them into correspondence with the spectrum of the Faddeev-Popov operator. In particular we shall make contact to task i) by studying the spectrum for semiclassical field configurations with non-trivial holonomy.