Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings

Abstract

It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model. The expression consists of a universal function constructed from the free energy of the refined topological string theory with an overall topological invariant characterizing the Calabi-Yau manifold. In this paper we explore two other superconformal Chern-Simons theories of the circular quiver type. We find that the partition function of one theory enjoys the same expression from the refined topological string theory as the ABJM matrix model with different topological invariants while that of the other is more general. We also observe an unexpected relation between these two theories.

35 pages, 1 figure; v2: section 3.3 added, references added

References in corpus (9)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Exact ABJM Partition Function from TBA
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Instanton Effects in Orbifold ABJM Theory

Cited by in corpus (9)

• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Fermi gas approach to general rank theories and quantum curves
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Geometric transition in Non-perturbative Topological string
• Duality Cascades and Affine Weyl Groups
• Duality Cascades and Parallelotopes