Cluster Transformations from Bipartite Field Theories

Franco, Sebastian

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: Feb 17, 2014
• Journal: Physical Review D - Particles, Fields, Gravitation, and Cosmology
• 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
• Public URL: https://durham-repository.worktribe.com/output/1464201