Abstract
We discuss the relation of quantum properties of d-dimensional and dimensionally reduced theories with a special emphasis on the use of a regularization accounting for power divergences. The main examples are N=1, d=10 super Yang-Mills (SYM 10 1) and N=1, d=11 supergravity (SG 11 1) and their reductions. In particular, we understand the vanishing of the one-loop β-function in SYM 4 4 (zero conformal anomalies in SG 4 8) as a consequence of the absence of L 6 ( L 7) power divergences in SYM 10 1(SG 11 1). The heat kernel expansion coefficients b 2 k , k=0,…, 3 are found to be zero for SG 11 1 (as well as for SYM 10 1 and SG 10 1 and thus the one-loop finiteness of maximal SGs in d⩽7 is explicity demonstrated. We also present the expressions for the one-loop constant gauge field effective lagrangian and scalar effective potential in the SYM 4 4 theory and analyse the problem of N=4 supersymmetry breaking.
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