Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories

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 (SYM101) and N=1, d=11 supergravity (SG111) and their reductions. In particular, we understand the vanishing of the one-loop β-function in SYM44 (zero conformal anomalies in SG48) as a consequence of the absence of L6 (L7) power divergences in SYM101(SG111). The heat kernel expansion coefficients b2k, k=0,..., 3 are found to be zero for SG111 (as well as for SYM101 and SG101 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 SYM44 theory and analyse the problem of N=4 supersymmetry breaking. © 1983.