  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.
