Holography Beyond the Penrose Limit

TL;DR

This paper develops a systematic quantization of interacting string theory beyond the Penrose limit, analyzing the spectrum of two-impurity states and testing holography by comparing string energies with gauge theory dimensions.

Contribution

It introduces a detailed light-cone gauge quantization method for interacting strings beyond the Penrose limit, including fermionic states and supermultiplet structure analysis.

Findings

Spectrum matches gauge theory at low orders of perturbation

Discrepancy appears at third order in perturbation theory

Method enables exploration of holography in more general backgrounds

Abstract

The flat pp-wave background geometry has been realized as a particular Penrose limit of AdS_5 x S^5. It describes a string that has been infinitely boosted along an equatorial null geodesic in the S^5 subspace. The string worldsheet Hamiltonian in this background is free. Finite boosts lead to curvature corrections that induce interacting perturbations of the string worldsheet Hamiltonian. We develop a systematic light-cone gauge quantization of the interacting worldsheet string theory and use it to obtain the interacting spectrum of the so-called `two-impurity' states of the string. The quantization is technically rather intricate and we provide a detailed account of the methods we use to extract explicit results. We give a systematic treatment of the fermionic states and are able to show that the spectrum possesses the proper extended supermultiplet structure (a non-trivial fact since half the supersymmetry is nonlinearly realized). We test holography by comparing the string energy spectrum with the scaling dimensions of corresponding gauge theory operators. We confirm earlier results that agreement obtains in low orders of perturbation theory, but breaks down at third order. The methods presented here can be used to explore these issues in a wider context than is specifically dealt with in this paper.