Brane Waves, Yang-Mills theories and Causality

TL;DR

This paper investigates the AdS/CFT correspondence by comparing Yang-Mills effective actions with supergravity potentials, revealing cancellations and causal effects consistent with theoretical predictions.

Contribution

It demonstrates the equivalence of supergravity potentials in AdS and flat space for constant gauge fields and explores causal retardation effects with time-dependent fields.

Findings

Supergravity potential matches flat space in specific conditions

Causal retardation effects are reflected in Yang-Mills acceleration terms

Lowest order acceleration terms agree with supergravity expectations

Abstract

We provide evidence for the validity of AdS/CFT correspondence in the Coulomb branch by comparing the Yang-Mills effective action with the potential between waves on two separated test 3-branes in the presence of a large number of other 3-branes. For constant gauge fields excited on the branes, this requires that the supergravity potential in a $AdS_5 \times S^5$ background is the {\it same} as that in flat space, despite the fact that both propagators and couplings of some relevant supergravity modes are different. We show that this is indeed true, due to a subtle cancellation. With time-dependent gauge fields on the test branes, the potential is sensitive to retardation effects of causal propagation in the bulk. We argue that this is reflected in higher derivative (acceleration) terms in the Yang-Mills effective action. We show that for two 3-branes separated in flat space the structure of lowest order acceleration terms is in agreement with supergravity expectations.