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

We address the issue of correspondence between classical supergravity and quantu, super Yang-Mills (or Matrix theory) expressions for the long-distance, low-velocity interaction potentials between 0-branes and bound states of branes. The leading-order potentials are reproduced by the F4 terms in the 1-loop SYM effective action. Using self-consistency considerations, we determine a universal combination of F6 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 18 supersymmetric 4⊥1 | 0 and 4⊥4⊥4 | 0 bound states representing external D = 5 and D = 4 black holes. We give explicit descriptions of these configurations in terms of 14 supersymmetric SYM backgrounds on dual tori. Under a proper choice of the gauge field backgrounds, the 2-loop F6 SYM action reproduces the full expression for the subleading term in the supergravity potentials, including its subtle v2 part.