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Aspects of ABJM orbifolds
High Energy Physics - Theory · Submitted 15 Sep 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study abelian and non-abelian orbifolds of the ABJM model. | contribution 0.97 | 0.93 | 0.03 | asserted 0.87 |
| s1 | 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. | method 0.64 | 0.96 | 0.11 | asserted 1.00 |
| s2 | 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. | interpretation 0.88 | 0.73 | 0.10 | asserted 1.00 |
| s3 | 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. | result 0.71 | 0.93 | 0.18 | asserted 1.00 |
| s4 | 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. | result 1.00 | 0.93 | 0.43 | asserted 1.00 |
| s5 | This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. | result 0.78 | 0.81 | 0.07 | asserted 1.00 |
| s6 | We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. | result 0.97 | 0.91 | 0.07 | asserted 1.00 |
| s7 | 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. | method 0.80 | 0.91 | 0.11 | asserted 0.99 |
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The paper
Original 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.
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How the literature uses it
13 arXiv papers cite this in 26 sentences
Papers citing it · 18 sentences without a confident label
Uses its method or tool 2 papers
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We used the approach on [ref] but using projective representations of $Γ$ which we showed is equivalent to twisting the crossed product algebra $𝒜_c⊠Γ$.
Aspects of ABJM orbifolds with discrete torsion · Conclusions · 0.83
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[equation] It is convenient to introduce a formal associative algebraic structure so that $X=⊕X_i,i+1$ etc, along the lines of [ref] (see also [ref] ).
Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra · Extremal chiral ring states are described by Young diagrams · 0.88
Cites it as support 2 papers
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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 $ℂ^4/(Γ×ℤ_|Γ|k)$ [ref] .
Integrability of Orbifold ABJM Theories · Introduction · 0.97
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It can also be checked that for any non-diagonal matrix, the off-diagonal modes become massive [ref] , thereby implying that the subspace of diagonal matrices is infact the entire moduli space of the theory.
AdS4/CFT3 : ABJM Theory, Brane Geometry, Correlators and Mellin Space · $𝒩 = 3$ CSM with Product Gauge group · 0.98
Cites it as background 4 papers
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Other orbifold ABJM theories are discussed in [ref] .
Integrability of Orbifold ABJM Theories · Introduction · 0.98
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Orbifolds of this type, for $Γ$ any A-D-E group, have been already considered [ref] and also many toric setups (see for example [ref] and references therein) along with some non-toric deformations [ref] .
Aspects of ABJM orbifolds with discrete torsion · Introduction · 0.97
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(For very recent work on orbifolds of the ABJM theory, see [ref] .) This leads us to construct an un-Higgsing algorithm where one starts with a QCS theory for a singularity $X$, and then enlarges the quiver in a specific way, corresponding to “blowing up” $X$.
(Un)Higgsing the M2-brane · Introduction and overview · 0.93
What it cites · 85 sentences without a confident label
Builds on 2 papers
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We consider a modification of the ABJM theory [ref] with $G=∏_i=1^2nU(N_i)$, described by Benna et al. in [ref] .
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · The BKKS example · 0.90
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We consider a modification of the ABJM theory [ref] with $G=∏_i=1^2nU(N_i)$, described by Benna et al. in [ref] .
Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence · The BKKS example · 0.90
Uses the method or tool of 4 papers
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For theories that have couplings of single trace type, there is a general recipe to build the moduli space from the components we have studied so far [ref] .
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua · The complete moduli space · 0.85
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We will use the notation of [ref] frequently in this paper.
Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence · Constructing the orbifold theories · 0.80
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If one builds an orbifold according to the prescription of Douglas and Moore [ref] , we have to gauge a discrete symmetry $Γ$.
D-branes, Quivers, and ALE Instantons · Constructing the orbifold theories · 0.91
Compares with 1 paper
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This monodromy is similar to fractional branes in orbifolds with discrete torsion [ref] where a similar monodromy of fractional branes is encountered, except that in that case the monodromy is already visible with perturbative gauge invariant operators and does not require monopole operators.
Discrete Torsion, AdS/CFT and duality · The chiral ring · 1.00
Cites as support 2 papers
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This is how the field theory tells us that the Chern-Simons terms are generated by fluxes [ref] .
A Stringy Origin of M2 Brane Chern-Simons Theories · Aspects of non abelian orbifolds · 0.98
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As shown in [ref] , one can also have fractional flux on all fluxes simultaneously.
The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus · The chiral ring · 0.97
Cites as background 17 papers
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These theories, whose first example was constructed in [ref] and which we will call the ABJM model, have the following properties that make them similar to their four dimensional cousins: * The theories posses an $N=2$ supersymmetry in three dimensions: these have a simple superspace description similar to the $N=1$ superspace in four dimensions. * The degrees of freedom are vector (super)fields and chiral superfields.
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.88
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This was originally suggested by Schwarz [ref] as a source of interesting dualities, but the examples with duals were found later in [ref] .
Superconformal Chern-Simons Theories · Introduction · 0.99
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For the case of the ABJM theory, these have been studied in various works [ref] .
A Nonperturbative Test of M2-Brane Theory · Introduction · 0.89
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