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

TL;DR

This paper explores the correspondence between supergravity and super Yang-Mills theories for long-distance brane interactions, identifying specific higher-order terms in SYM that match supergravity predictions, including subleading velocity contributions.

Contribution

It determines a universal combination of F^6 terms in 2-loop SYM that reproduces subleading supergravity interaction potentials for various brane configurations.

Findings

2-loop F^6 SYM terms match supergravity subleading potentials

Explicit SYM backgrounds describe extremal black hole bound states

Correct reproduction of velocity-dependent terms in supergravity

Abstract

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 0-branes and various bound states of branes. The leading-order potentials are known to be 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 410 and 4440 bound states representing extremal D=5 and D=4 extremal 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 v^2 part.