7 Divergence Properties of Maximal Supergravity 

In general, the larger the number of supersymmetries, the tamer the ultraviolet divergences because of the tendency for these to cancel between bosons and fermions in a supersymmetric theory. In four-dimensions maximal N =8 supergravity may therefore be expected to be the least divergent of all possible supergravity theories. Moreover, the maximally supersymmetric gauge theory, N =4 super-Yang-Mills, is completely finite [129, 97, 80], leading one to suspect that the superb ultraviolet properties of N =4 super-Yang-Mills would then feed into improved ultra-violet properties for N =8 supergravity via its relation to gauge theory. This makes the ultraviolet properties of N =8 supergravity the ideal case to investigate first via the perturbative relationship to gauge theory.

• 7.1 One-loop cut construction
• 7.2 Higher loops
• 7.3 Divergence properties of N =8 supergravity

Perturbative Quantum Gravity and its Relation to Gauge Theory Zvi Bern http://www.livingreviews.org/lrr-2002-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de