Dimension-two vacuum condensates in gauge-invariant theories

Much attention has recently been drawn to the vacuum condensates (0 vertical bar A(mu)(a2)vertical bar 0) and (0 vertical bar(c) over bar (a)c(a)vertical bar 0) in nonAbelian gauge theories. It is believed that these condensates contain information about nonperturbative phenomena in quantum chromodynamics, such as quark confinement [1]. They contribute to the nonperturbative parts of the gluon (2) and the quark [3] propagators. It was suggested in [1] that the gluon condensate may be sensitive to various topological defects such as Dirac strings and monopoles. The condensates considered are vacuum expectation values (VEVs) of gauge-dependent operators, which makes calculating observable effects problematic. It was shown in [4], [5] that if the Yang-Mills theory. is considered as a limit of a (regularized) noncommutative gauge-invariant theory, then the VEV (integral d(4)x A(mu)(2)) is independent of the choice of gauge and can therefore have a direct physical meaning This proof depends essentially on the existence of a gauge-invariant regularization of noncommutative theories, which needs further investigation. It is therefore interesting to explore the gauge invariance of dimension-two condensates in the commutative theory to study the question of its possible contribution to the Wilson operator product expansion (OPE). A partial answer to this question in the Abelian theory case was given in [4]. Here, we continue to investigate this problem in both the Abelian and the non-Abelian cases, and we address the problem of the Wilson OPE in the noncommutative theory.