AdS/CFT in the Infinite Momentum Frame

TL;DR

This paper explores the duality between gravity in pp-wave spacetimes on extremal branes and conformal field theories in the infinite momentum frame, providing evidence that the CFT resolves bulk singularities and analyzing related symmetries.

Contribution

It demonstrates the duality between pp-wave AdS spacetimes and CFTs in the infinite momentum frame, and investigates the implications for singularity resolution and symmetries.

Findings

The horizon of extremal branes is a singularity experienced by geodesic observers.

The decoupling limit yields a pp-wave in AdS, exemplified by the Kaigorodov spacetime.

The scalar 2-point function is constant at leading order, supporting the duality conjecture.

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.