Integrability of Orbifold ABJM Theories

Abstract

Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma (\simeq {\mathbb{Z}}_n)<SU(4{)}_R\times U(1{)}_b$. For general $\Gamma$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations. The eigenvalues of the anomalous dimension matrix are also obtained. For $\Gamma <SU(4)$, two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this framework.

33 pages, 9 figures

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• Finite-size Effect for Dyonic Giant Magnons in $C{P}_{\beta }^3$