Hilbert Series of Bipartite Field Theories

Abstract

We study the algebraic structure of the mesonic moduli spaces of bipartite feld theories by computing the Hilbert series. Bipartite feld theories form a large family of 4d N = 1 supersymmetric gauge theories that are defned by bipartite graphs on Riemann surfaces with boundaries. By calculating the Hilbert series, we are able to identify the generators and defning generator relations of the mesonic moduli spaces of these theories. Moreover, we show that certain bipartite feld theories exhibit enhanced global symmetries which can be identifed through the computation of the corresponding refned Hilbert series. As part of our study, we introduce two one-parameter families of bipartite feld theories defned on cylinders whose mesonic moduli spaces are all complete intersection toric Calabi-Yau 3-folds.