Cluster Transformations from Bipartite Field Theories
High Energy Physics - Theory
2015-06-12 v2 Mathematical Physics
Algebraic Geometry
Combinatorics
math.MP
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.
Cite
@article{arxiv.1301.0316,
title = {Cluster Transformations from Bipartite Field Theories},
author = {Sebastian Franco},
journal= {arXiv preprint arXiv:1301.0316},
year = {2015}
}
Comments
v2: 19 pages, 6 figures. Accepted for publication in PRD