BPS amplitudes, helicity supertraces and membranes in M-theory

We study BPS dominated loop amplitudes in M-theory on T-2. For this purpose we generalize the concept of helicity supertraces to nine spacetime dimens ions. These traces distinguish between various massive supermultiplets and appear as coefficients in their one-loop contributions to n-graviton scatte ring amplitudes. This can be used to show that only ultrashort BPS multiple ts contribute to the R-4 term in the effective action, which was first comp uted by Green, Gutperle and Vanhove. There are two inequivalent ultrashort BPS multiplets which describe the Kaluza-Klein states and the wrapped membr anes that cover the torus a number of times. From the perspective of the ty pe-II strings they correspond to momentum and winding states and D0 or D1 b ranes. (C) 2000 Elsevier Science B.V. All rights reserved.