(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF) × SUR(NF) symmetry breaking in QCD
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, RU-141980, Dubna, Moscow Region, Russia
2 Institute for Theoretical Physics, University of Erlangen-Nürnberg, Staudtstrasse 7, D-91058, Erlangen, Germany
Published online: 27 February 2005
It is shown that an (anti-) self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates,, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.
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