Long-distance interactions of branes: Correspondence between supergravity and super Yang-Mills descriptions

We address the issue of correspondence between classical supergravity and quantum super Yang-Mills (or Matrix theory) expressions for the long-distance, low-velocity interaction potentials between O-branes and bound states of branes. The leading-order potentials are reproduced by the F-4 terms in the l-loop SYM effective action. Using self-consistency considerations, we determine a universal combination of F-6 terms in the 2-loop SYM effective action that corresponds to the subleading terms in the supergravity potentials in many cases, including O-brane scattering off 1/8 supersymmetric 4 perpendicular to 1 parallel to 0 and 4 perpendicular to 4 perpendicular to 4 parallel to 0 bound states representing extremal D = 5 and D = 4 black holes. We give explicit descriptions of these configurations in terms of 1/4 supersymmetric SYM backgrounds on dual tori. Under a proper choice of the gauge field backgrounds, the 2-loop F-6 SYM action reproduces the full expression for the subleading term in the supergravity potentials, including its subtle upsilon(2) part. (C) 1998 Elsevier Science B.V.