(Un)Higgsing the M2-brane

James Sparks; Nessi Benishti; Yang-Hui He

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(Un)Higgsing the M2-brane

Nessi Benishti, Yang-Hui He, James Sparks

High Energy Physics - Theory · Submitted 24 Sep 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).

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We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof. In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaining a plethora of new models. In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing.	contribution 0.85	0.86	0.09	speculative 0.50
s1	In particular we study in detail the orbifold C^4/Z_2^3, obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof.	contribution 0.89	0.95	0.09	asserted 1.00
s2	In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaining a plethora of new models.	contribution 0.51	0.95	0.21	asserted 1.00
s3	In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).	result 0.50	0.90	0.24	asserted 1.00

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The paper

Original abstract

We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof. In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaining a plethora of new models. In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3
hep-th 2011-05 conditional novelty 6.0 of 10

Reducing M-theory on a circle yields Chern-Simons quiver gauge theories dual to AdS4 x Y^{p,q}(CP2) for the full range of q and for every torsion G4 flux, with ranks and levels that differ from the earlier equal-rank ...
Chiral flavors and M2-branes at toric CY4 singularities
hep-th 2009-11 conditional novelty 6.0 of 10

Chirally flavored N=2 Chern-Simons quivers reproduce toric Calabi-Yau fourfolds with codimension-two singularities, via a conjectured quantum F-term relation between diagonal monopole operators and bifundamental fields.

How the literature uses it

17 arXiv papers cite this in 61 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 40 sentences without a confident label

Builds on it 2 papers

In addition to the matching found for the $Q^1,1,1$ and $Y^1,2(ℂℙ^2)$ geometries, we extend the computation of $H^4_tor(Y^1,2(ℂℙ^2),)$ in [ref] to a one-parameter family of smooth $Y_7$ which includes $Y^1,2(ℂℙ^2)$, and check that the type IIB brane computation of $n$ and the algebraic topology computation of $H^4(Y_7,)$ match in such a class, in agreement with the physical expectation.

Type IIB construction of flavoured ABJ(M) and fractional M2 branes · Introduction · 0.95
We also performed unHiggsing of theories with adjoints, extending the results of [ref] to reach certain phases of the known theories $𝒞_3$ and $𝒞_5$.

On the Higgsing and UnHiggsing of Fano 3-Folds · UnHiggsing Fano 3-Folds · 0.96

Compares with it 2 papers

These results, which are straightforward to derive using branes in type IIB string theory, agree with the more complicated cohomological analysis of [ref] .

Type IIB construction of flavoured ABJ(M) and fractional M2 branes · Fractional M2 branes and partial resolutions · 0.92
Let us pause to highlight the difference between the approach of [ref] and that of, for example, [ref] , [ref] .

On the Higgsing and UnHiggsing of Fano 3-Folds · Higgsing and UnHiggsing of Fano 2 Folds · 0.99

Cites it as background 8 papers

The beautiful interplay of torsion G-fluxes in the M-theory backgrounds and partial resolutions of Calabi-Yau fourfold singularities was investigated in detail by Benishti, He and Sparks in [ref] .

Type IIB construction of flavoured ABJ(M) and fractional M2 branes · Fractional M2 branes and partial resolutions · 0.91
The supergravity dual of this RG flow was first discussed in the Type IIB context by Klebanov-Witten [ref] , and to some extent in the M-theory AdS$_4 ×Y^7$ context in [ref] .

Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence · Introduction · 0.85
UnHiggsing M2-brane theories was systematically explored in [ref] to which we refer the reader for more details.

On the Higgsing and UnHiggsing of Fano 3-Folds · UnHiggsing Fano 3-Folds · 0.90

What it cites · 100 sentences without a confident label

Builds on 2 papers

Motivated by this early work of [ref] on partial resolutions of $^3/_2^2$ and $^3/_3^2$, here we study the Abelian orbifold $^4/_2^3$.

D-Brane Gauge Theories from Toric Singularities and Toric Duality · Introduction and overview · 0.84
Motivated by this early work of [ref] on partial resolutions of $^3/_2^2$ and $^3/_3^2$, here we study the Abelian orbifold $^4/_2^3$.

D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds · Introduction and overview · 0.84

Uses the method or tool of 4 papers

The GLSM equations (from the $Q_t$-matrix) are derived[Alternatively, these were derived by hand in [ref] .] easily with the aid of the forward algorithm: |p_6|^2+|p_1|^2+ |p_2|^2-|p_3|^2-|p_4|^2-|p_5|^2 = 0 , 2|p_1|^2+|p_2|^2-|p_3|^2-|p_4|^2-|p_5|^2 = ζ .

Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3 · $C(Y^1,2(ℂℙ^2))_II$ : Some puzzles · 0.86
The construction of the VMS outlined in Subsection [ref] was turned into an algorithm in [ref] , whose end product is precisely the lattice points of $Δ$, together with their multiplicities.

M2-Branes and Quiver Chern-Simons: A Taxonomic Study · The QCS forward algorithm · 0.86
First, we devised a general un-Higgsing algorithm for toric quiver-Chern-Simons theories, in analogy to [ref] .

Unhiggsing the del Pezzo · Summary and prospects · 0.80

Compares with 2 papers

Notice this is distinct from Seiberg duality in $(3+1)$ dimensions, and dualities in $(2+1)$ dimensions that were observed in [ref] , in that the quiver is unchanged, and only the CS levels are altered.

3D Seiberg-like Dualities and M2 Branes · Dualities · 0.83
Notice this agrees with [ref] , where the cohomology groups of $Y_UV$ were computed via a completely different method.

Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3 · $Y^1,2(ℂℙ^2)$: Gravity results · 0.99

Cites as background 31 papers

A key breakthrough was made in [ref] , following work by [ref] , in which Aharony-Bergman-Jafferis-Maldacena (ABJM) constructed a $U(N)_k×U(N)_-k$ quiver-Chern-Simons (QCS) theory, with $𝒩=6$ superconformal symmetry, and conjectured this to be the low-energy theory on $N$ M2-branes probing a $^4/_k$ singularity.

Algebraic structures on parallel M2-branes · Introduction and overview · 0.96
A key breakthrough was made in [ref] , following work by [ref] , in which Aharony-Bergman-Jafferis-Maldacena (ABJM) constructed a $U(N)_k×U(N)_-k$ quiver-Chern-Simons (QCS) theory, with $𝒩=6$ superconformal symmetry, and conjectured this to be the low-energy theory on $N$ M2-branes probing a $^4/_k$ singularity.

Comments on Multiple M2-branes · Introduction and overview · 0.96
A key breakthrough was made in [ref] , following work by [ref] , in which Aharony-Bergman-Jafferis-Maldacena (ABJM) constructed a $U(N)_k×U(N)_-k$ quiver-Chern-Simons (QCS) theory, with $𝒩=6$ superconformal symmetry, and conjectured this to be the low-energy theory on $N$ M2-branes probing a $^4/_k$ singularity.

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction and overview · 0.96

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