SU(N) instantons and their condensation in the field-strength approach

A 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 ((h) over bar expansion), in particular the same instanton physics. However, the field-strength formulation offers a simple non-perturbative treatment which results in the so-called FSA. This approach already includes a good deal of quantum fluctuations of the standard formulation. In order to explicitly establish the connection between both approaches 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 = 1/6N(N-2 - 1). For this class of instantons we prove that instanton-type configurations of localized field strength cease to exist as stationary points of the FSA action. At the same time homogeneous classical solutions emerge which have the same color and Lorentz structure as the SU(N) Yang-Mills instantons. Furthermore these instanton-generated FSA solutions are those of lowest action. In this way we provide evidence that the homogeneous FSA vacuum may be interpreted as a solid of condensed instantons aligned in color and Lorentz space.