Network and Seiberg Duality

TL;DR

This paper introduces a new class of 4d N=1 superconformal quiver gauge theories linked to planar bipartite networks, classifies their IR fixed points via Grassmannian permutations, and extends the framework to Riemann surfaces.

Contribution

It defines a novel connection between bipartite networks, Grassmannian cells, and superconformal theories, extending the classification to bordered Riemann surfaces.

Findings

IR fixed points classified by Grassmannian permutations

Generalization to Riemann surfaces with geometric data

Insights into IR R-charges and superconformal indices

Abstract

We define and study a new class of 4d N=1 superconformal quiver gauge theories associated with a planar bipartite network. While UV description is not unique due to Seiberg duality, we can classify the IR fixed points of the theory by a permutation, or equivalently a cell of the totally non-negative Grassmannian. The story is similar to a bipartite network on the torus classified by a Newton polygon. We then generalize the network to a general bordered Riemann surface and define IR SCFT from the geometric data of a Riemann surface. We also comment on IR R-charges and superconformal indices of our theories.