The structure of UV divergences in SS YM theories

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