PP-Waves and Holography

TL;DR

This paper explores holography in the pp-wave limit of AdS5×S5, analyzing mode correspondence and boundary theory deformations, and outlines a method for computing correlation functions in this setting.

Contribution

It investigates the holographic structure in the pp-wave limit, identifying the roles of different modes and proposing a holographic calculation procedure.

Findings

Normalizable modes correspond to states in the boundary theory.

Non-normalizable modes relate to boundary deformations.

Additional non-normalizable modes lack clear super-Yang-Mills interpretation.

Abstract

We consider aspects of holography in the $pp$-wave limit of $AdS_5\times S5$. This geometry contains two $\RR4$'s, one obtained from $AdS_5$ directions, and the other from the $S 5$. We argue that the holographic direction in the $pp$-wave background can be taken to be $r$, the radial direction in the first $\RR4 $. Normalizable modes correspond to states, and non-normalizable modes correspond to deformations of the boundary theory. In the strict $pp$-wave limit, there are additional non-normalizable modes in the second $\RR 4$, which have no apparent super-Yang-Mills interpretation. We outline the procedure for calculating correlation functions holographically.