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 lo ng-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-consiste ncy 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 a nd 4 perpendicular to 4 perpendicular to 4 parallel to 0 bound states representing extremal D = 5 and D = 4 black holes. We give explicit de scriptions of these configurations in terms of 1/4 supersymmetric SYM backgrounds on dual tori. Under a proper choice of the gauge field bac kgrounds, the 2-loop F-6 SYM action reproduces the full expression for the subleading term in the supergravity potentials, including its sub tle upsilon(2) part. (C) 1998 Elsevier Science B.V.