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M2Branes and Quiver ChernSimons: A Taxonomic Study
, 2008
"... We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphsising a succinct “forward algorithm”. Few “order parametres ” are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotent ..."
Abstract

Cited by 40 (13 self)
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We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphsising a succinct “forward algorithm”. Few “order parametres ” are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2branes probing toric CalabiYau 4folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly
Imperial/TP/08/AH/10 M2Branes and Quiver ChernSimons: A Taxonomic Study
, 811
"... We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphsising a succinct “forward algorithm”. Few “order parametres ” are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotent ..."
Abstract
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We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphsising a succinct “forward algorithm”. Few “order parametres ” are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2branes probing toric CalabiYau 4folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly
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"... Abstract: Recent paper arXiv:1103.0553 studied the quiver gauge theories on coincident M2 branes on a singular toric CalabiYau 4folds which are complex cone over toric Fano 3folds. There are 18 toric Fano manifolds but only 14 toric Fano were obtained from the forward algorithm. We attempt to sys ..."
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Abstract: Recent paper arXiv:1103.0553 studied the quiver gauge theories on coincident M2 branes on a singular toric CalabiYau 4folds which are complex cone over toric Fano 3folds. There are 18 toric Fano manifolds but only 14 toric Fano were obtained from the forward algorithm. We attempt to systematize the inverse algorithm which helps in obtaining quiver gauge theories on M2branes from the toric data of the CalabiYau 4folds. In particular, we obtain quiver gauge theories on coincident M2branes corresponding to the remaining 4 toric Fano 3folds. We observe that these quiver gauge theories cannot be given a dimer tiling presentation.
Partial resolution of complex cones over Fano B
"... In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2branes probing the singularities of special kind of CalabiYau fourfolds which were complex cones over toric Fano P3, B1, B2, B3. These quiver gauge theories cannot be given a dimer ..."
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In our recent paper arXiv:1108.2387, we systematized inverse algorithm to obtain quiver gauge theory living on the M2branes probing the singularities of special kind of CalabiYau fourfolds which were complex cones over toric Fano P3, B1, B2, B3. These quiver gauge theories cannot be given a dimer tiling presentation. We use the method of partial resolution to show that the toric data of C4 and Fano P3 can be embedded inside the toric data of Fano B theories. This method indirectly justifies that the two node quiver ChernSimons theories corresponding to C4, Fano P3 and their orbifolds can be obtained by higgsing matter fields of