Holographic Reformulation of String Theory on AdS_5 x S^5 background in the PP-wave limit

TL;DR

This paper proposes a holographic interpretation of string theory in the Penrose limit of AdS_5 x S^5, resolving puzzles related to time interpretation by connecting bulk string S-matrix with boundary correlation functions.

Contribution

It introduces a tunneling null geodesic approach to interpret PP-wave strings, linking bulk string S-matrix with boundary super Yang-Mills correlators, extending holographic principles.

Findings

Predicts a direct identification of bulk string S-matrix with boundary correlators.

Shows the necessity of infinite contact terms in string field theory for holography.

Provides a consistent framework respecting supersymmetry.

Abstract

The recent proposal on the correspondence between the ${\cal N}=4$ super Yang-Mills theory and string theory in the Penrose limit of the AdS$_5\times$S$^5$ geometry involves a few puzzles from the viewpoint of holographic principle, especially in connection with the interpretation of times. To resolve these puzzles, we propose to interpret the PP-wave strings on the basis of tunneling null geodesics connecting boundaries of the AdS geometry. Our approach predicts a direct and systematic identification of the S-matrix of Euclidean string theory in the bulk with the short-distance structure of correlation functions of super Yang-Mills theory on the AdS boundary, as an extension of the ordinary relation in supergravity-CFT correspondence. Holography requires an infinite number of contact terms for interaction vertices of string field theory and constrains their forms in a way consistent with supersymmetry.