BPS Amplitudes, Helicity Supertraces and Membranes in M-Theory

TL;DR

This paper investigates BPS loop amplitudes in M-theory on T^2, introducing generalized helicity supertraces in nine dimensions to identify contributions of specific supermultiplets to the effective action.

Contribution

It extends helicity supertrace concepts to nine dimensions and shows only ultrashort BPS multiplets contribute to the R^4 term in M-theory on T^2.

Findings

Only ultrashort BPS multiplets contribute to R^4 term

Identifies two types of ultrashort BPS multiplets: Kaluza-Klein and membrane states

Connects supermultiplet types to string theory states like momentum, winding, and branes

Abstract

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 dimensions. These traces distinguish between various massive supermultiplets and appear as coefficients in their one-loop contributions to n-graviton scattering amplitudes. This can be used to show that only ultrashort BPS multiplets contribute to the R^4 term in the effective action, which was first computed by Green, Gutperle and Vanhove. There are two inequivalent ultrashort BPS multiplets which describe the Kaluza-Klein states and the wrapped membranes that cover the torus a number of times. From the perspective of the type-II strings they correspond to momentum and winding states and D0 or D1 branes.