A Note on the Partition Function of ABJM theory on S^3

Abstract

We study the partition function Z of U(N)_k x U(N)_{-k} Chern-Simons matter theory (ABJM theory) on S^3 which is recently obtained by the localization method. We evaluate the eigenvalue integral in Z exactly for the N=2 case. We find that Z has a different dependence on k for even k and odd k. We comment on the possible implication of this result in the context of AdS/CFT correspondence.

16 pages; v2: introduction slightly changed, v3: minor corrections

Cited by in corpus (35)

• Non-perturbative effects and the refined topological string
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• Instanton Bound States in ABJM Theory
• Exact Results on the ABJM Fermi Gas
• Membrane instantons from a semiclassical TBA
• A note on perturbation series in supersymmetric gauge theories
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Higgs branch localization of 3d N=2 theories
• Solving M-theory with the Conformal Bootstrap
• Direct derivation of "mirror" ABJ partition function
• Exact ABJM Partition Function from TBA
• ABJ Fractional Brane from ABJM Wilson Loop
• ABJM Wilson Loops in Arbitrary Representations
• The Partition Function of ABJ Theory
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Instanton Effects in Orbifold ABJM Theory
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• Exact relations between M2-brane theories with and without Orientifolds
• Exact Instanton Expansion of ABJM Partition Function
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• ABJ Wilson loops and Seiberg Duality
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• SU(N) q-Toda equations from mass deformed ABJM theory
• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• 3d superconformal indices and isomorphisms of M2-brane theories
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• N=2 Chern-Simons-Matter Theories Without Vortices
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas