Holography Beyond the Penrose Limit

TL;DR

This work develops a systematic light-cone quantization of curvature corrections to the AdS5×S5 string beyond the Penrose limit, focusing on the two-impurity sector. It derives the interacting string spectrum via the GS action expanded to order ${ m O}(R^{-2})$, computes the one-loop perturbative corrections across bosonic, fermionic, and mixed sectors, and verifies PSU(2,2|4) multiplet structure. The string energies are matched against gauge-theory anomalous dimensions, yielding agreement at one and two loops but a breakdown at three loops, which stimulates discussion of integrability and possible refinements. The all-orders-in-${ m ilde{eta}}$ results for the two-impurity spectrum provide a strong test-bed for holography beyond the Penrose limit and highlight the subtle interplay between worldsheet dynamics and gauge theory data.

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.