Finite size corrections and integrability of mathcal N=2 SYM and DLCQ strings on a pp-wave

We compute the planar finite size corrections to the spectrum of the dilatation operator acting on two-impurity states of a certain limit of conformal N = 2 quiver gauge field theory which is a Z_M-orbifold of N = 4 supersymmetric Yang-Mills theory. We match the result to the string dual, IIB superstrings propagating on a pp-wave background with a periodically identi¯ed null coordinate. Up to two loops, we show that the computation of operator dimensions, using an effective Hamiltonian technique derived from renormalized perturbation theory and a twisted Bethe ansatz which is a simple generalization of the Beisert-Dippel-Staudacher [1] long range spin chain, agree with each other and also agree with a computation of the analogous quantity in the string theory. We compute the spectrum at three loop order using the twisted Bethe ansatz and ¯nd a disagreement with the string spectrum very similar to the known one in the near BMN limit of N = 4 super-Yang-Mills theory. We show that, like in N = 4, this disagreement can be resolved by adding a conjectured "dressing factor" to the twisted Bethe ansatz. Our results are consistent with integrability of the N = 2 theory within the same framework as that of N = 4