Abstract
The conjectured duality between type IIB string theory on AdS5 x S5 and N = 4 SU(Nc) super Yang-Mills theory in four dimensions simplifies in the Penrose limit or, in other words, when the string's angular momentum is large. As the string action in this limit is solvable, it is possible to go beyond the supergravity approximation and compare exact string energies with the anomalous dimensions of a sector of large R-charge operators. This equivalence should of course extend to the full AdS5 x S5 space and to operators of finite R-charge. We take some modest steps in this direction by expanding the full string action in inverse powers of the angular momentum and finding the first order perturbative corrections to the energy spectrum. These corrections reproduce the gauge theory anomalous dimensions for a range of different operators to two-loops in the 't Hooft parameter but disagree at three-loops. Furthermore, these near-plane wave results are useful in studying the recently discovered integrability in this AdS/CFT system and can be used to motivate the form of quantum string scattering matrices.
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