No abstract

The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial-wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effective action. Our approach works for any quark-mass and interpolates smoothly between the analytically known small and large mass expansions.

Renormalization of pure Yang-Mills theory is studied in the so-called Abelian gauge, a special bilinear gauge with a favored role given to a certain Abelian subgroup from the full non-Abelian gauge group. Renormalization in this gauge exhibits some unusual features-notably, different wave-function renormalizations are necessary for gauge fields with different "Abelian" charges and quartic ghost interaction terms are generated as renormalization counterterms. Despite these difficulties we show, through a careful analysis of the Becchi-Rouet-Stora transformation properties of the effective action, that Yang-Mills theory can be consistently renormalized in this gauge. Possible physical applications of this type of gauge (and its generalization which renders a favored role to a certain non-Abelian subgroup from the given gauge group) are noted briefly.

Fermion zero modes around a general multivortex background are analyzed in supersymmetrized self-dual (Maxwell-) Chern-Simons Higgs systems, using the index theorem and other means. In the models with an N=2 extended supersymmetry, a simple connection is established between all independent fermion zero modes and corresponding bosonic zero modes. We provide a supersymmetry-based explanation of the result.