journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-29journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-29journal_title: Journal of Physics A: Mathematical and Theoretical article_type: paper article_title: Consistency and derangements in brane tilings copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-03-22 date_accepted: 2016-07-06 date_epub: 2016-07-2

Amihay Hanany

Beil C

Benvenuti S

Bocklandt R

Broomhead N

Butti A

Cameron P

Davison B

Feng B

Franco S

Garcia-Etxebarria I

Grothendieck A

Hanany A

Kenyon R

Koch R D M

Mikhalkin G

Rak-Kyeong Seong

Sanjaye Ramgoolam

Uranga A M

Vishnu Jejjala

Journal of Physics A Mathematical and Theoretical

arXiv

Hanany, A

Jejjala, V

Ramgoolam, S

Seong, R-K

Queen Mary Research Online

Consistency and derangements in brane tilings

Brane tilings describe Lagrangians (vector multiplets, chiral multiplets, and the superpotential) of four-dimensional 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

Hanany, Amihay

Jejjala, Vishnu

Ramgoolam, Sanjaye

Seong, Rak-Kyeong

ScholarWorks@UNIST

Crossref

https://qmro.qmul.ac.uk/xmlui/bitstream/123456789/12114/4/Ramgoolam%20Consistency%20and%20Derangements%202016%20Accepted.pdf.pdf

Consistency and derangements in brane tilings

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Queen Mary Research Online

ScholarWorks@UNIST

Crossref