Integrability of orbifold ABJM theories

Integrable structure has played a very important role in the study of various non-perturbative aspects of planar Aharony-Bergman-Jafferis-Maldacena (ABJM) theories. In this paper, we showed that this remarkable structure survives after orbifold operation with discrete group Gamma < SU(4)(R) x U(1)(b). For general Gamma(similar or equal to Z(n)), we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations (BAEs). 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.Special Fund for Theoretical Physics from NSFC [11447613]; NSFC [11575202, 11475116, 11222549]; K.C.Wong Education FoundationSCI(E)ARTICLE1