AdS/CFT in the Infinite Momentum Frame

TL;DR

This work analyzes pp-waves propagating on extremal non-dilatonic branes and demonstrates the resulting pp-curvature singularities at the horizon, suggesting a boundary where the spacetime terminates. In the decoupling limit these configurations become pp-waves in AdS, with Kaigorodov spacetime as a canonical example, posited to be dual to a conformal field theory in the infinite momentum frame with constant momentum density. The authors compute the boundary energy-momentum tensor, show a null, momentum-dense state, and use AdS/CFT to determine scalar 2-point functions under the remaining conformal symmetries, finding results consistent with the infinite momentum frame and independent of the background momentum density to leading order in $1/N^2$. The discussion extends to a Virasoro symmetry in higher dimensions arising from AdS$_3$ submanifolds and contemplates how the boundary CFT might resolve bulk singularities, with implications for brane-world models like Randall-Sundrum and for the interpretation of bulk gravitons. Overall, the paper provides evidence supporting the Kaigorodov/CFT duality and sheds light on the role of infinite momentum frame dynamics in holography, including potential avenues to understand singularity resolution in string theory.

Abstract

This paper considers the spacetimes describing pp-waves propagating on extremal non-dilatonic branes. It is shown that an observer moving along a geodesic will experience infinite curvature at the horizon of the brane, which should therefore be regarded as singular. Taking the decoupling limit of these brane-wave spacetimes gives a pp-wave in AdS, the simplest example being the Kaigorodov spacetime. It has been conjectured that gravity in this spacetime is dual to a CFT in the infinite momentum frame with constant momentum density. If correct, this implies that the CFT must resolve the singularity of the bulk spacetime. Evidence in favour of this conjecture is presented. The unbroken conformal symmetries determine the scalar 2-point function up to an arbitrary function of one variable. However, an AdS/CFT calculation shows that this function is constant (to leading order in $1/N^2$) and the result is therefore the same as when the full conformal symmetry is unbroken. This paper also discusses a recently discovered Virasoro symmetry of metrics describing pp-waves in AdS and naked singularities in the Randall-Sundrum scenario.