On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.Comment: 32 pages, latex, 7 EPS figures. v2: references, comments added, typos corrected, incorrect `skeleton' conjecture in sect. 3 replaced by a more careful treatment. v3: typos corrected, final version published in JHE