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Inverse algorithm and M2-brane theories. (English) Zbl 1306.81220

Summary: A recent paper [J. Davey et al., J. Phys. A, Math. Theor. 44, No. 40, Article ID 405401, 104 p. (2011; Zbl 1229.81230)] studied the quiver gauge theories on coincident \(M2\) branes on a singular toric Calabi-Yau 4-folds which are complex cone over toric Fano 3-folds. 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 \(M2\)-branes from the toric data of the Calabi-Yau 4-folds. In particular, we obtain quiver gauge theories on coincident \(M2\)-branes corresponding to the remaining 4 toric Fano 3-folds. We observe that these quiver gauge theories cannot be given a dimer tiling presentation.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
16G20 Representations of quivers and partially ordered sets
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies

Citations:

Zbl 1229.81230
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References:

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