On lightcone string field theory from Super Yang-Mills and holography

TL;DR

This paper explores the holographic duality between Super Yang-Mills theory and string theory in a pp-wave background, proposing a matrix model description and analyzing string interactions via SYM diagrams and Hamiltonian diagonalization.

Contribution

It introduces a matrix model derived from SYM's KK modes to describe the holographic dual of the pp-wave and analyzes string interactions within this framework.

Findings

Holographic dual of pp-wave has a one-dimensional boundary.

String interactions can be modeled by SYM diagrams and Hamiltonian perturbation.

Leading amplitude behaviors in SYM and string theory are in agreement.

Abstract

We investigate the issues of holography and string interactions in the duality between SYM and the pp wave background. We argue that the Penrose diagram of the maximally supersymmetric pp-wave has a one dimensional boundary. This fact suggests that the holographic dual of the pp-wave can be described by a quantum mechanical system. We believe this quantum mechanical system should be formulated as a matrix model. From the SYM point of view this matrix model is built out of the lowest lying KK modes of the SYM theory on an $S^3$ compactification, and it relates to a wave which has been compactified along one of the null directions. String interactions are defined by finite time amplitudes on this matrix model. For closed strings they arise as in AdS-CFT, by free SYM diagrams. For open strings, they arise from the diagonalization of the hamiltonian to first order in perturbation theory. Estimates of the leading behaviour of amplitudes in SYM and string theory agree, although they are performed in very different regimes. Corrections are organized in powers of $1/(\mu \alpha ' p^+)^2$ and $g^2(\mu \alpha ' p^+)^4$.