Exact results on ABJ theory and the refined topological string

Abstract

We study the partition function of the ABJ theory, which is the N=6 superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local P^1 x P^1, including membrane instanton effects in the M-theory dual.

24+29 pages, 4 figures; v2:minor improvements

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• The Refined Topological Vertex
• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Exact ABJM Partition Function from TBA
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Instanton Effects in Orbifold ABJM Theory

Cited by in corpus (15)

• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Probing non-perturbative effects in M-theory
• Topological Strings and Quantum Spectral Problems
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• ABJ Wilson loops and Seiberg Duality
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• ABJ Quadrality
• A Note on Instanton Effects in ABJM Theory
• The spectral problem of the ABJ Fermi gas
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• 3d dualities with decoupled sectors and brane transitions
• Subleading Corrections in N=3 Gaiotto-Tomasiello Theory