U-duality and D-brane combinatorics

We investigate D-brane instanton contributions to R4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutperle and Vanhove, we derive the non-perturbative O(e−1/λ) corrections to R4 couplings by a sequence of T-dualities, and interpret them as precise configurations of bound states of D-branes wrapping cycles of the compactification torus. Dp-branes explicitly appear as fluxes on D(p+2)-branes, and as gauge instantons on D(p+4)-branes. Specific rules for weighting these contributions are obtained, which should carry over to more general situations. Furthermore, it is shown that U-duality in D≤6 relates these D-brane configurations to O(e−1/λ2) instantons for which a geometric interpretation is still lacking.