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Aspects of ABJM orbifolds with discrete torsion
High Energy Physics - Theory · Submitted 22 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . | contribution 1.00 | 0.91 | 0.05 | asserted 0.92 |
| s1 | Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. | method 0.98 | 0.58 | 0.05 | asserted 1.00 |
| s2 | 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. | result 1.00 | 0.87 | 0.41 | asserted 1.00 |
| s3 | 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. | result 0.99 | 0.85 | 0.52 | asserted 1.00 |
| s4 | Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. | result 0.95 | 0.88 | 0.26 | asserted 1.00 |
| s5 | We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian. | contribution 1.00 | 0.92 | 0.10 | asserted 0.97 |
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The paper
Original 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.
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How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 58 sentences without a confident label
Uses the method or tool of 7 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 · Conclusions · 0.83
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The moduli spaces we found can be seen as a $ℂ^*$-fibration over a basis described by $𝒵𝒜$, so we can use the same reasoning as in [ref] .
Discrete Torsion, AdS/CFT and duality · Matching with gravity duals · 0.93
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The moduli spaces we found can be seen as a $ℂ^*$-fibration over a basis described by $𝒵𝒜$, so we can use the same reasoning as in [ref] .
Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua · Matching with gravity duals · 0.93
Compares with 6 papers
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These seem quite different from the deformed backgrounds obtained in [ref] , but there is no contradiction.
On deformed gauge theories and their string/M-theory duals · Matching with gravity duals · 0.98
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Like in the type IIB case [ref] they are related by mirror symmetry.
Conifolds with Discrete Torsion and Noncommutativity · Matching with gravity duals · 0.87
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Like in the type IIB case [ref] they are related by mirror symmetry.
Discrete Torsion, AdS/CFT and duality · Matching with gravity duals · 0.87
Cites as background 25 papers
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In this section we review the well known orbifold construction for D-branes [ref] and how to introduce discrete torsion [ref] on them.
On Conformal Theories in Four Dimensions · The Orbifold projection · 0.99
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In this section we review the well known orbifold construction for D-branes [ref] and how to introduce discrete torsion [ref] on them.
D-branes and Discrete Torsion · The Orbifold projection · 0.99
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In this section we review the well known orbifold construction for D-branes [ref] and how to introduce discrete torsion [ref] on them.
D-branes and Discrete Torsion II · The Orbifold projection · 0.99
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