String Theory Origin of Bipartite SCFTs

TL;DR

This paper embeds N=1 superconformal field theories from bipartite graphs into string theory, linking them to Argyres-Douglas theories and geometric structures like the Grassmannian, revealing dualities and IR fixed point classifications.

Contribution

It introduces a string theory construction for bipartite SCFTs, connecting them to algebraic curves, brane configurations, and the Grassmannian, and explores their dualities and IR fixed points.

Findings

Realization of N=1 SCFTs via brane configurations

Classification of IR fixed points using the Grassmannian

Evidence linking line operator VEVs to Grassmannian coordinates

Abstract

We provide a string theory embedding for N = 1 superconformal field theories defined by bipartite graphs inscribed on a disk. We realize these theories by exploiting the close connection with related N = 2 generalized (A_(k-1), A_(n-1)) Argyres-Douglas theories. The N = 1 theory is obtained from spacetime filling D5-branes wrapped on an algebraic curve and NS5-branes wrapped on special Lagrangians of C^2 which intersect along the BPS flow lines of the corresponding N = 2 Argyres-Douglas theory. Dualities of the N = 1 field theory follow from geometric deformations of the brane configuration which leave the UV boundary conditions fixed. In particular we show how to recover the classification of IR fixed points from cells of the totally non-negative Grassmannian Gr^(tnn)_(k,n+k). Additionally, we present evidence that in the 3D theory obtained from dimensional reduction on a circle, VEVs of line operators given by D3-branes wrapped over faces of the bipartite graph specify a coordinate system for Gr^(tnn)_(k,n+k).