(Un)Higgsing the M2-brane

Benishti, Nessi; He, Yang‐Hui; Sparks, James

doi:10.1007/jhep01(2010)067

Cited by 18 publications

(53 citation statements)

References 107 publications

(358 reference statements)

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“…Let us also note that the base Y 7 of the cone is a smooth manifold only if each face of the toric diagram is a triangle, and there are no lattice points internal to any edge or face. These conditions are equivalent [56] to the cone being good, in the sense of [54].…”

Section: Jhep01(2014)083mentioning

confidence: 99%

Wilson loops and the geometry of matrix models in AdS4/CFT3

Farquet

Sparks

2014

J. High Energ. Phys.

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We study a general class of supersymmetric AdS 4 × Y 7 solutions of M-theory that have large N dual descriptions as N = 2 Chern-Simons-matter theories on S 3 . The Hamiltonian function h M for the M-theory circle, with respect to a certain contact structure on Y 7 , plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle, giving a fundamental string in AdS 4 , is supersymmetric precisely at the critical points of h M , and moreover the value of this function at the critical point determines the M2-brane action. Such a configuration determines the holographic dual of a BPS Wilson loop for a Hopf circle in S 3 , and leads to an effective method for computing the Wilson loop on both sides of the correspondence in large classes of examples. We find agreement in all cases, including for several infinite families, and moreover we find that the image h M (Y 7 ) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h M mapping to points where the derivative of the eigenvalue density is discontinuous.

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Section: Jhep01(2014)083mentioning

confidence: 99%

Wilson loops and the geometry of matrix models in AdS4/CFT3

Farquet

Sparks

2014

J. High Energ. Phys.

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“…However it should be mentioned here that unlike the abelian orbifolds of C 3 , the (2+1)-dimensional quiver gauge theories (and hence Q F , Q D ) for general orbifolds (Z n 1 × Z n 2 × Z n 3 ) of C 4 are not known. In [34], the quiver theories for C 4 / (Z 2 ) 3 were obtained, but a general method for constructing quiver Chern-Simons theories for an arbitrary orbifold of C 4 is not clear. Hence the method of partial resolution of C 4 orbifolds to obtain the quiver theories for any given Calabi-Yau fourfold is not applicable.…”

Section: Introductionmentioning

confidence: 99%

“…Some of these embeddings were discussed in [39]. Using the methods of higgsing [40,41] and unhiggsing [34], it was shown in [39], that the toric diagram of the complex cones over Fano threefolds can be embedded into Calabi-Yau fourfolds which may or may not be complex cones over Fano threefolds. We also made a small progress in [42], where we studied the partial resolution of Fanos B 1 , B 2 , B 3 , B 4 .…”

Section: Introductionmentioning

confidence: 99%

Embedding and partial resolution of complex cones over Fano threefolds

Dwivedi

2016

Annals of Physics

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This work deals with the study of embeddings of toric Calabi-Yau fourfolds which are complex cones over the smooth Fano threefolds. In particular, we focus on finding various embeddings of Fano threefolds inside other Fano threefolds and study the partial resolution of the latter in hope to find new toric dualities. We find many diagrams possible for many of these Fano threefolds, but unfortunately, none of them are consistent quiver theories. We also obtain a quiver Chern-Simons theory which matches a theory known to the literature, thus providing an alternate method of obtaining it.Comment: version to be publishe

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“…e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]). Even though nice parallels are drawn between the familiar case of D3-branes probing Calabi-Yau threefold singularities and the present circumstance of M2-branes probing Calabi-Yau fourfold singularities, the latter situation is far less understood.…”

Section: Introductionmentioning

confidence: 99%

“…Complications arise in the various analogues of the wealth of properties enjoyed by the D3-brane, such as singularityresolution in relation to (un)Higgsing, the "inverse algorithm" for systematically constructing the world-volume gauge theory, Seiberg duality, etc. Part of the issue arises from the new possibility of turning on G-fluxes on torsion-cycles in the dual AdS geometry [20,21,23].…”

Section: Introductionmentioning

confidence: 99%

Probing the space of toric quiver theories

Hewlett

2010

J. High Energ. Phys.

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We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. We examine some preliminary statistics on this space of toric quiver theories.

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(Un)Higgsing the M2-brane

Cited by 18 publications

References 107 publications

Wilson loops and the geometry of matrix models in AdS4/CFT3

Wilson loops and the geometry of matrix models in AdS4/CFT3

Embedding and partial resolution of complex cones over Fano threefolds

Probing the space of toric quiver theories

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