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

Abstract

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 $\mathcal{N}=2$ quiver gauge field theory which is a $Z_M$-orbifold of $\mathcal{N}=4$ 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~\cite{Beisert:2004hm} 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 $\mathcal{N}=4$ super-Yang-Mills theory. We show that, like in $\mathcal{N}=4$, this disagreement can be resolved by adding a conjectured ``dressing factor'' to the twisted Bethe ansatz. Our results are consistent with integrability of the $\mathcal{N}=2$ theory within the same framework as that of $\mathcal{N}=4$.

arXiv comment28 pages

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• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• The scaling function at strong coupling from the quantum string Bethe equations
• Finite Size Giant Magnon
• Bethe Ansatz Equations for General Orbifolds of N=4 SYM
• Finite-size corrections to the rotating string and the winding state
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• Phases of Thermal N=2 Quiver Gauge Theories