Holograms of Branes in the Bulk and Acceleration Terms in SYM Effective Action

TL;DR

This paper provides concrete evidence that exchange of supergravity modes with nonzero momentum in AdS/CFT correspondence is encoded in derivative terms of the gauge theory effective action, matching calculations of brane interactions.

Contribution

It explicitly calculates the force between branes due to non-zero momentum supergravity mode exchange and confirms its consistency with the gauge theory effective action and non-renormalization.

Findings

Force matches flat space calculations

Supports the encoding of supergravity effects in gauge theory derivatives

Consistent with non-renormalization of acceleration terms

Abstract

If the AdS/CFT correspondence is valid in the Coulomb branch, the potential between waves on a pair of test branes in the bulk should be reproduced by the relevant Yang-Mills theory effective action on the boundary. Earlier work has provided evidence for this in the case of constant gauge field brane waves. In this paper we provide concrete evidence for an earlier proposal that the effects of exchange of supergravity modes with nonzero momentum in the brane directions are encoded in certain terms involving derivatives of the field strength in the gauge theory effective action. We explicitly calculate the force quadratic in the field strengths coming from the exchange of non-zero momentum two form fields between two 3-branes in $AdS_5 \times S^5$ to lowest nontrivial order in the momentum. We show that this is exactly the same as that between the branes living in flat space. The result is in agreement with the gauge theory effective action and consistent with the non-renormalization property of this term. We comment on the relationship of other ``acceleration'' terms in the SYM effective action with quantities in supergravity.