The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.
BPS Amplitudes, Helicity Supertraces and Membranes in M-Theory
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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.
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Taxonomy of Instanton Corrections in Infinite Distance Limits
The Schwinger integral over light towers captures precisely the instantons with actions in the window (Λ_sp/M_light)^{-1} ≤ S_inst ≤ Λ_sp/M_light, as verified in eight- and seven-dimensional toroidal compactifications.