New Directions in Bipartite Field Theories

TL;DR

This paper explores Bipartite Field Theories (BFTs), introducing new methods for assigning gauge symmetries, determining moduli spaces, and generating theories, with a focus on non-planar graphs and their geometric properties.

Contribution

It presents a novel approach to gauge symmetry assignment, a procedure for moduli space determination, and systematic graph reduction methods for BFTs, expanding the class of theories studied.

Findings

Matroid polytope matches toric diagram for disk graphs

New systematic prescription for graph reduction

Generation of new theories from existing graphs

Abstract

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d N=1 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning gauge symmetries to graphs. A new procedure is introduced in order to determine the toric Calabi-Yau moduli spaces of BFTs. For graphs on a disk, we show that the matroid polytope for the corresponding cell in the Grassmannian coincides with the toric diagram of the BFT moduli space. A systematic BFT prescription for determining graph reductions is presented. We illustrate our ideas in infinite classes of BFTs and introduce various operations for generating new theories from existing ones. Particular emphasis is given to theories associated to non-planar graphs.