Aspects of ABJM orbifolds with discrete torsion

Abstract

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup Γ of SU(2) × SU(2) . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order m of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of m in addition to the other effects that were found before in the literature. Therefore we got a Zk|Γ| m action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where Γ is abelian.