Aspects of ABJM orbifolds with discrete torsion

TL;DR

This paper studies how discrete torsion affects orbifolds of the ABJM theory, revealing that the cocycle order influences the moduli space and the M-theory fiber structure, especially for abelian groups.

Contribution

It provides a detailed analysis of the impact of discrete torsion on ABJM orbifolds, including the role of cocycle order and the resulting moduli space modifications.

Findings

The cocycle order m affects the moduli space structure.

Discrete torsion modifies the M-theory fiber by a factor of m.

A detailed analysis of abelian orbifold cases is presented.

Abstract

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . 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 $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian.