Abstract
Using the background-field method, covariant supergraphs and infrared subtraction techniques we analyse the structure of the higher-loop ultraviolet divergences in supersymmetric Yang-Mills theories. We show that in regularization by dimensional reduction they are given by a specific gauge invariant term constructed outof the vector connection and that they can be obtained by analyzing a special subset of all possible supergraphs. From the structure of the divergences we are able to conclude that in supersymmetric theories if the self-energies of the quantum fields in the presence of the background are finite up to L loops the YM background effective action is finite at ( L + 1) loops.
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