Branes probing black holes

TL;DR

The paper analyzes the dynamics of a D-brane probe near a black-brane background by comparing the gauge-theory effective action (obtained from integrating out massive stretched strings) with the probe action in supergravity. In the decoupling and large-$N$ limits, it shows that leading one-loop interactions in the gauge theory reproduce the corresponding gravity results, including $F^4$-type terms and velocity- and static-force contributions, across extremal and near-extremal cases. It further connects these results to Matrix theory and DLCQ, discusses nonperturbative corrections that interpolate to 11D/M-theory descriptions, and argues for a general correspondence that constrains higher-loop contributions. Overall, the work provides concrete evidence for the gauge/gravity correspondence in brane-black-hole systems and clarifies how nonlinear gravitational dynamics emerge from large-$N$ gauge theories, with implications for Matrix theory and nonperturbative string theory.

Abstract

We consider a brane moving close to a large number of coincident branes. We compare the calculation of the effective action using the gauge theory living on the brane and the calculation using the supergravity approximation. We discuss some general features about the correspondence between large N gauge theories and black holes. Then we do a one loop calculation which applies for extremal and near extremal black holes. We comment on the expected results for higher loop calculations. We make some comments on the Matrix theory interpretation of these results.