Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach

Abstract

We study the partition function of three-dimensional $\mathcal{N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as $Z(N)=e^A{C}^{-1/3}\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of $B$ for general $\mathcal{N}=4$ theories, a conjectural form of $A$ for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.

36 pages, 4 figures; v2: typos corrected and clarifications added

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• Fractional M2-branes
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• N=4 Chern-Simons theories and wrapped M-branes in their gravity duals
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Cited by in corpus (12)

• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• ABJM Matrix Model and 2D Toda Lattice Hierarchy
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Duality Cascades and Affine Weyl Groups
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• Duality Cascades and Parallelotopes
• 3d dualities with decoupled sectors and brane transitions
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas