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Higgsing M2-brane Theories
High Energy Physics - Theory · Submitted 27 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Connections between different M2-brane theories are established via the Higgs mechanism, which can be most efficiently studied on brane tilings.
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The abstract, sentence by sentence
Connections between different M2-brane theories are established via the Higgs mechanism, which can be most efficiently studied on brane tilings. This leads to several M2-brane models, with brane tilings or Chern-Simons levels which have not been considered so far. The moduli spaces of these models are identified and examined in detail. The toric diagrams are constructed using Kasteleyn matrices and the forward algorithm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Connections between different M2-brane theories are established via the Higgs mechanism, which can be most efficiently studied on brane tilings. | method 0.49 | 0.29 | 0.21 | asserted 1.00 |
| s1 | This leads to several M2-brane models, with brane tilings or Chern-Simons levels which have not been considered so far. | contribution 0.76 | 0.79 | 0.21 | asserted 0.99 |
| s2 | The moduli spaces of these models are identified and examined in detail. | contribution 0.75 | 0.90 | 0.16 | asserted 1.00 |
| s3 | The toric diagrams are constructed using Kasteleyn matrices and the forward algorithm. | method 0.99 | 0.83 | 0.06 | asserted 1.00 |
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The paper
Original abstract
Connections between different M2-brane theories are established via the Higgs mechanism, which can be most efficiently studied on brane tilings. This leads to several M2-brane models, with brane tilings or Chern-Simons levels which have not been considered so far. The moduli spaces of these models are identified and examined in detail. The toric diagrams are constructed using Kasteleyn matrices and the forward algorithm.
Human review
References
How the literature uses it
25 arXiv papers cite this in 58 sentences
Papers citing it · 34 sentences without a confident label
Uses its method or tool 4 papers
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If the fugacity $s_α$ is assigned to the perfect matching $p_α$, then the Hilbert series of the mesonic moduli space can be computed by the usual Molien-Weyl formula [ref] : (s_α; X) = ∮∏^c-G-2_i=1 z_i/2πi z_i ∮∏^G-2_j=1 b_j/2 πi b_j 1/∏^c_α=1(1- s_αZ_α(z_i, b_j)), where $G$ is the number of gauge groups of the theory and $Z_α(z_i, b_j)$ represents the monomial weight of the perfect matching $p_α$ under the fugacities $z_i$, coming from linear relations among the perfect matchings, and $b_j$, arising from the D-terms.
M2-Branes and Fano 3-folds · The R-charges · 0.98
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By adopting the forward algorithm for Chern-Simons brane tilings [ref] [cf. forward algorithm for $4d$ quiver gauge theories in appendix app_mesonic.], the level matrix $C$ then is econc10 C=( cc U(1)_1 U(1)_2 1 1 1 -1 ) , and econc11 d = Q̃ ·P^t , Q_F = (P) , Q_D = (C)·Q̃ , Q_t = (Q_F Q_D) →G_t = (Q_t) .
Double Handled Brane Tilings · Conclusions and Future Directions · 1.00
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We introduce an integer number $n_a$ for each link in the Tiling in such a way that [equation] where $d^a_i=±1$ is the $U(1)$ charge of the field corresponding to the link [ref] .
Parameter spaces of massive IIA solutions · The quiver · 0.98
Compares with it 4 papers
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These values of the CS levels mean that the theory is not the $ℬ_4$ theory of [ref] , although it has the same quiver and tiling description.
On the Higgsing and UnHiggsing of Fano 3-Folds · M2-brane Theories Without a Brane Tiling Description · 0.98
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While this result is strictly valid only for isolated singularities, we note it coincides with the conjecture in [ref] .
Baryonic symmetries in AdS_4/CFT_3: an overview · Global symmetries in $AdS_4/CFT_3$ and their spontaneous breaking · 0.93
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These values are consistent with the results of [ref] , but different from [ref], [ref].
Black holes with baryonic charge and $\mathcal{I}$-extremization · Baryonic symmetry · 0.98
Cites it as support 1 paper
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Additional geometrical arguments for why the ABJM theory describes $N$ M2-branes on $^4/_k$ are presented in [ref] .
M2-branes and AdS/CFT · Non-Abelian Chern-Simons theory · 0.98
Cites it as background 12 papers
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The study of $= 2$ quiver Chern-Simons theories dual to Calabi-Yau cones was initiated in [ref] , followed by a large number of works [ref] .
Chiral flavors and M2-branes at toric CY4 singularities · Introduction · 0.97
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The works of [ref] have brought about tremendous interest in the M2-brane, and following [ref] , where the world-volume theory was realised as a Chern-Simons quiver theory in $(2+1)$-dimensions, much activity ensued (q.v. e.g. [ref] ).
Probing the Space of Toric Quiver Theories · Introduction · 0.99
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By studying the world volume gauge theories of probe $D3$-branes and $M2$-branes, various toric singularities were identified and classified [ref] .
Symmetries of Abelian Orbifolds · Discussions and Prospects · 0.98
What it cites · 68 sentences without a confident label
Builds on 3 papers
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However, it is easy to generalise the result for $k>1$; several explicit examples are given in [ref] .
Brane Tilings and M2 Branes · A Summary of The $𝒩=2$ Supersymmetric Chern–Simons Theory · 0.83
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However, it is easy to generalise the result for $k>1$; several explicit examples are given in [ref] .
Partition Functions for Membrane Theories · A Summary of The $𝒩=2$ Supersymmetric Chern–Simons Theory · 0.83
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However, it is easy to generalise the result for $k>1$; several explicit examples are given in [ref] .
Tilings, Chern-Simons Theories and M2 Branes · A Summary of The $𝒩=2$ Supersymmetric Chern–Simons Theory · 0.83
Uses the method or tool of 10 papers
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Next [ref] , let us compute the Hilbert series of the divisor corresponding to $p_1$, which we will refer to as $D_1$.
Brane Tilings and M2 Branes · A summary of the $M^1,1,1$ theory · 0.87
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Then, the fractional brane charges can be obtained using the method described in [ref] : ch (F_1) = (-1, 0 ,0), ch(F_2) = (0, 1, 0), ch (F_3) = (1, -1, 1) , where the 3 entries are the D4-brane charge on $^1_1$, the D4-brane charge on $^1_2$, and the D2-brane charge respectively.
Quiver Theories from D6-branes via Mirror Symmetry · The $SPP$ theory with $k$ units of RR 2-form fluxes on both $^1$'s · 0.99
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We summarise the process leading to the toric diagram, which is given by the $G_t$ matrix, in the flow chart forward [ref] .
M2-Branes and Quiver Chern-Simons: A Taxonomic Study · The Forward Algorithm · 0.88
Uses data or values from 5 papers
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The Hilbert series is derived in [ref] : (t, ^4/_k) = 1+t^2+2kt^k - 2kt^k+2 - t^2k - t^2k+2/(1-t^2)^3(1-t^k)^2 , where $t$ is the fugacity for R-charges (in the unit of 1/2).
Tilings, Chern-Simons Theories and M2 Branes · The conifold theory with $k$ units of RR 2-form flux on $^1$ · 0.88
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The mesonic Hilbert series of $×$ is given by (4.14) of [ref] : (t_1,t_2,x_1,x_2; ×) = ∑^∞_i=0 t^i_2 ∑^∞_n=0 [n;n] t^2n_1 .
Phases of M2-brane Theories · The $_0 ×$ theory from giving a VEV to one of $X^i_23$, $X^i_41$ · 0.95
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Each of the 4 nodes in the quiver diagram (f:phase1f0) corresponds to a collection of fractional branes, whose charges are given respectively as (see (4.15) of [ref] ): ch(F_1) = (-1, 1,0, 0), ch(F_2) = (1, -1, 1, -1), ch(F_3) = (1, 0, -1, 0), ch(F_4) = (-1,0, 0,0) , Let us denote by $k_1$ and $k_2$ the RR 2-form fluxes on $^1_1$ and $^1_2$, and by $k_4$ the RR 4-form flux on $^1 ×^1$.
Quiver Theories from D6-branes via Mirror Symmetry · The $_0$ theory with $k$ units of RR 4-form flux on $^1 ×^1$ · 0.98
Compares with 4 papers
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Setting $k=1$, we recover the formula (6.23) of [ref] .
Phases of M2-brane Theories · The $_0$ theory with $k$ units of RR 4-form flux on $^1 ×^1$ · 0.80
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Note that in 3+1 dimensions, these quiver and tiling correspond to Phase II of the $_0$ theory [ref] .
Master Space, Hilbert Series and Seiberg Duality · A summary of Phase II of $Q^1,1,1/_2$ (the $𝒮_2 𝒪_2$ model) · 0.86
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Note that in 3+1 dimensions, these quiver and tiling correspond to Phase II of the $_0$ theory [ref] .
The Master Space of N=1 Gauge Theories · A summary of Phase II of $Q^1,1,1/_2$ (the $𝒮_2 𝒪_2$ model) · 0.86
Cites as background 39 papers
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A $U(N) ×U(N)$ Chern–Simons (CS) theory at level $(k, -k)$ with bi-fundamental matter fields was subsequently proposed by Aharony, Bergman, Jafferis and Maldacena (ABJM) [ref] as a model describing $N$ M2-branes in the $^4/_k$ orbifold background.
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.95
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Considerable progress in understanding theories for multiple M2-branes in various backgrounds has been taking place since the works by Bagger–Lambert [ref] and Gustavsson [ref] .
Modeling Multiple M2's · Introduction · 1.00
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Considerable progress in understanding theories for multiple M2-branes in various backgrounds has been taking place since the works by Bagger–Lambert [ref] and Gustavsson [ref] .
Algebraic structures on parallel M2-branes · Introduction · 1.00
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