U-DUALITY AND D-BRANE COMBINATORICS

We investigate D-brane instanton contributions to R-4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutpe rle and Vanhove, we derive the non-perturbative O(e(-1/lambda 2)) corr ections to R-4 couplings by a sequence of T-dualities, and interpret t hem as precise configurations of bound states of D-branes wrapping cyc les of the compactification torus. Dp-branes explicitly appear as flux es on D(p + 2)-branes, and as gauge instantons on D(p + 4)-branes. Spe cific rules for weighting these contributions are obtained, which shou ld carry over to more general situations. Furthermore, it is shown tha t U-duality in D less than or equal to 6 relates these D-brane configu rations to O(e(-1/lambda?2)) instantons for which a geometric interpre tation is still lacking. (C) 1998 Elsevier Science B.V.