Aspects of ABJM orbifolds

Abstract

We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic monopole operators. These determine the chiral ring of the theory, and thus they provide the complete set of order parameters determining the classical vacua of the theory. We show that the proper quantization of these semiclassical solutions gives us the topology of moduli space, including the additional quotient information due to the Chern-Simons levels. In general, we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group, even in the non-abelian case. This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We also show that the problem of the moduli space can be much more easily analyzed by using the method of images and representation theory of crossed product algebras rather than dealing only with the quiver theory data.

Integrability of orbifold ABJM theories

“…Finally we analyse the condition on the charges for the orbifolding to preserve N = 2 and N = 4 supersymmetries. We also confirm these results by using the fact that the orbifold ABJM theory is the low energy effective theory of N membranes placed at the orbifold singularity C 4 /(Γ × Z |Γ|k ) [37].…”

“…We further demonstrate this method is indeed correct by counting the spinors of SO(8) preserved by the orbifold. Notice that the orbifold ABJM theory is the low energy effective theory of N coincident M2-branes at C 4 /(Γ × Z |Γ|k ) orbifold singularity where |Γ| is the order of Γ and Z |Γ|k acts as overall phase rotations of the four complex coordinates [37]. Under the action of the generator of finite group Γ as for generic t 2 , t 3 and n, and this demonstrates our conclusion above 7 .…”

“…In [34], two concrete quiver gauge theories with the residual N = 4 supersymmetries (nonchiral orbifold) and N = 2 supersymmetries (chiral orbifold) have been established through two different Z n orbifoldings in ABJM field theory. Other orbifold ABJM theories are discussed in [35][36][37]. In this paper, we only consider the case that Γ is isomorphic to Z n .…”

Finite-size effect for dyonic giant magnons inCPβ3

“…Formally identifying this open string as closed string leads us to consider Z M orbifolding of ABJM theory. This theory appears when we consider low energy effective theory of N M 2 branes put at C 4 /(Z M × Z M k ) orbifold singularity [25]- [28] with Z M acting on C 4 as…”

Half-BPS M2-brane orbifolds

“…It is hoped that progress in this direction may be aided by our description of these new orbifolds in terms of iterated quotients in order to perhaps obtain dual N = 4 superconformal field theories for some of them via a projection of the known theories (e.g. via further orbifolding or orientifolding), perhaps along the lines discussed in [37].…”