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).
Highlights
A striking feature of string theory is the simple geometric characterization it provides of diverse quantum field theories in various dimensions
Thanks to the mathematical results of [8] for bicolored graphs, these fixed points are classified by decorated permutations, which in turn are specified by cells in the totally non-negative Grassmannian Grtkn,nn+k
Compactifying the 4D spacetime on the geometry S(1t) × M Cq with M Cq a Melvin cigar geometry, we show that in the small S(1t) limit, these operators are closely related to line operators of the N = 2 Argyres-Douglas theory
Summary
A striking feature of string theory is the simple geometric characterization it provides of diverse quantum field theories in various dimensions. The specification of a cell in the totally non-negative Grassmannian provides a simple way to characterize possible Seiberg dual phases, that is, the equivalence class of bipartite networks which define the same IR fixed point. Once the deformations of the geometry are switched on, the one-cycles of the intersection correspond to a network of BPS flows which preserve a fixed N = 1 subalgebra of the N = 2 supersymmetry algebra Given such a one-dimensional network, there exists a unique set of special Lagrangians in C2 which intersect Σ, realizing our quiver gauge theories. This provides a powerful way to characterize possible IR fixed points of the quiver gauge theories. One of our tasks in this paper will be to give a simple explanation for these relations from a brane construction in string theory
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