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, lowvelocity interaction potentials between 0-branes and bound states of branes. The leading-order potentials are reproduced by the F 4 terms in the 1-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 0-brane scattering off 1/8 supersymmetric 4⊥1‖0 and 4⊥4⊥4‖0 bound states representing extremal D = 5 and D = 4 black holes. We give explicit descriptions of the 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 v2 part. E-mail: [email protected] Also at Lebedev Physics Institute, Moscow. E-mail: [email protected]