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@article{Hanany:2016:35/355401,
author = {Hanany, A and Jejjala, V and Ramgoolam, S and Seong, R-K},
doi = {35/355401},
journal = {Journal of Physics A - Mathematical and Theoretical},
title = {Consistency and derangements in brane tilings},
url = {http://dx.doi.org/10.1088/1751-8113/49/35/355401},
volume = {49},
year = {2016}
}

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TY  - JOUR
AB  - Brane tilings describe Lagrangians (vector multiplets, chiral multiplets, and the superpotential) of four-dimensional ${ \mathcal N }=1$ supersymmetric gauge theories. These theories, written in terms of a bipartite graph on a torus, correspond to worldvolume theories on N D3-branes probing a toric Calabi–Yau threefold singularity. A pair of permutations compactly encapsulates the data necessary to specify a brane tiling. We show that geometric consistency for brane tilings, which ensures that the corresponding quantum field theories are well behaved, imposes constraints on the pair of permutations, restricting certain products constructed from the pair to have no one-cycles. Permutations without one-cycles are known as derangements. We illustrate this formulation of consistency with known brane tilings. Counting formulas for consistent brane tilings with an arbitrary number of chiral bifundamental fields are written down in terms of delta functions over symmetric groups.
AU  - Hanany,A
AU  - Jejjala,V
AU  - Ramgoolam,S
AU  - Seong,R-K
DO  - 35/355401
PY  - 2016///
SN  - 1751-8113
TI  - Consistency and derangements in brane tilings
T2  - Journal of Physics A - Mathematical and Theoretical
UR  - http://dx.doi.org/10.1088/1751-8113/49/35/355401
VL  - 49
ER  -

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Amihay Hanany

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