Network and Seiberg Duality

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.

28 pages, 28 figures; v2: minor corrections

References in corpus (7)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Brane Tilings
• Brane Tilings and Their Applications
• Quivers, YBE and 3-manifolds
• Brane Tilings and Specular Duality
• Emergent 3-manifolds from 4d Superconformal Indices
• Exactly marginal deformations of quiver gauge theories as seen from brane tilings

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