Instanton Condensation in Field Strength Formulated QCD

Abstract

Field strength formulated Yang-Mills theory is confronted with the traditional formulation in terms of gauge fields. It is shown that both formulations yield the same semiclassics, in particular the same instanton physics. However, at the tree level the field strength approach is superior because it already includes a good deal of of quantum fluctuations of the standard formulation. These quantum fluctuations break the scale invariance of classical QCD and give rise to an instanton interaction and this causes the instantons to condense and form a homogeneous instanton solid. Such the instanton solids show up in the field strength approach as homogeneous (constant up to gauge transformations) vacuum solutions. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color structure and carry winding number $n=N(N^{2}-1)/6$. These instantons generate (after condensation) the lowest action solutions of the field strength approach. The statistical weight (entropy) of different homogeneous solutions for SU(3) is numerically estimated by Parisi's stochastic quantization method. Finally, we compare instanton induced quark condensation with the condensation of quarks in the homogeneous field strength solutions. Our investigations show that the homogeneous vacuum of the field strength approach simulates in an efficient way a condensate of instantons.