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

Astolfi, D., Grignani, G., Forini, V. & Semenoff, Gordon W (2006). Finite size corrections and integrability of N=2 SYM and DLCQ strings on a pp-wave. Journal of High Energy Physics(9), 056.. doi: 10.1088/1126-6708/2006/09/056

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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 Script N = 2 quiver gauge field theory which is a ZM-orbifold of Script 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 identified 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 find a disagreement with the string spectrum very similar to the known one in the near BMN limit of Script N = 4 super-Yang-Mills theory. We show that, like in Script 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 Script N = 2 theory within the same framework as that of Script N = 4.

Item Type: Article
Uncontrolled Keywords: Penrose limit and pp-wave background, AdS-CFT Correspondence
Divisions: School of Engineering & Mathematical Sciences

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