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.

arXiv comment36 pages, 4 figures; v2: typos corrected and clarifications added

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Cited by in corpus (39)

• Instanton effects in ABJM theory with general R-charge assignments
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Localization at large N in Chern-Simons-matter theories
• A profusion of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories
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• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
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• Giambelli Identity in Super Chern-Simons Matrix Model
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• Two-Point Functions in ABJM Matrix Model
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• ABJ Theory in the Higher Spin Limit
• M2-branes and $\mathfrak{q}$-Painlevé equations
• Jacobi-Trudi Identity in Super Chern-Simons Matrix Model
• Exact results for Wilson loops in orbifold ABJM theory
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