Superconformal Chern-Simons Theories from del Pezzo Geometries

Abstract

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.

arXiv comment47 pages; v3: typos corrected, published version

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• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Hanany-Witten Transition in Quantum Curves
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• Fermi gas approach to general rank theories and quantum curves
• Two-Point Functions in ABJM Matrix Model
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• Brane Transitions from Exceptional Groups
• Duality Cascades and Affine Weyl Groups
• Duality Cascades and Parallelotopes
• Quantum mirror curve of periodic chain geometry
• Quantum Mirror Map for Del Pezzo Geometries