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Superconformal Chern-Simons Theories from del Pezzo Geometries
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We present an explicit expression for the grand potential of the U(N)^3 superconformal Chern-Simons theory with the Chern-Simons levels being (k,0,-k). From the viewpoint of the Newton polygon, it is expected that the grand potential is given by the free energy of the topological string theory on the local D_5 del Pezzo geometry, though the explicit identification was a puzzle for years. We show how the expectation is realized explicitly. As a bonus, we can also study the Z_2 orbifold of this theory and find the grand potential is now given in terms of the local E_7 del Pezzo geometry.
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Cited by 2 Pith papers
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Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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Finiteness and Uniqueness of Duality Cascades in Three Dimensions for Affine Quivers
For affine D and E quiver Chern-Simons theories, duality cascades terminate uniquely only under large-rank restrictions because the associated polytope tiles the parameter space with gaps.
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