AdS/CFT in the Infinite Momentum Frame

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.

32 pages LaTeX. Corrected a typo, added a section on supersymmetry, comments on the implications of our analysis for the Randall-Sundrum scenario, and a brief discourse about free field theory and the ambiguity in the 2-point function

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