Brane tilings are efficient mnemonics for Lagrangians of N=2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the Kasteleyn technique is described which is conjectured to compute the three dimensional toric diagram of the non-compact moduli space of a single probe. The Hilbert Series is used to compute the spectrum of non-trivial scaling dimensions for a selected set of examples.
Hanany, A., Vegh, D., Zaffaroni, A. (2009). Brane tilings and M2 branes. JOURNAL OF HIGH ENERGY PHYSICS, 2009(3) [10.1088/1126-6708/2009/03/012].
Brane tilings and M2 branes
ZAFFARONI, ALBERTO
2009
Abstract
Brane tilings are efficient mnemonics for Lagrangians of N=2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the Kasteleyn technique is described which is conjectured to compute the three dimensional toric diagram of the non-compact moduli space of a single probe. The Hilbert Series is used to compute the spectrum of non-trivial scaling dimensions for a selected set of examples.
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