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Cluster Transformations from Bipartite Field Theories

Franco, Sebastian

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Authors

Sebastian Franco



Abstract

Bipartite field theories (BFTs) are a new class of 4D N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face weights under square moves in the graph. In this context, we obtain them by connecting regular parametrizations of the master space of the associated BFTs. For BFTs on a disk, these transformations follow from the properties of coordinates in the Grassmannian. This represents a new addition to the list of combinatorial objects for the Grassmannian, such as matching and matroid polytopes, that have been shown to emerge from BFT dynamics.

Citation

Franco, S. (2013). Cluster Transformations from Bipartite Field Theories. Physical Review D, 88(10), Article 105010. https://doi.org/10.1103/physrevd.88.105010

Journal Article Type Article
Publication Date Nov 8, 2013
Deposit Date Jan 27, 2014
Publicly Available Date Mar 29, 2024
Journal Physical Review D
Print ISSN 1550-7998
Electronic ISSN 1550-2368
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 88
Issue 10
Article Number 105010
DOI https://doi.org/10.1103/physrevd.88.105010

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