Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas

Abstract

We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact expression of the overall constant, which corresponds to the constant map in the topological string theory.

23 pages, 4 figures; v2: section 4.2 added, one figure added

References in corpus (11)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Atomic Classification of 6D SCFTs
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Probing non-perturbative effects in M-theory
• Exact ABJM Partition Function from TBA
• M-theoretic matrix models
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Instanton Effects in Orbifold ABJM Theory
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• 3d mirror symmetry as a canonical transformation

Cited by in corpus (22)

• Instanton effects in ABJM theory with general R-charge assignments
• The $\mathcal{N}=2$ Schur index from free fermions
• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Localization at large N in Chern-Simons-matter theories
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifolding of the ABJ Fermi gas
• 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
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Giambelli Identity in Super Chern-Simons Matrix Model
• Probing non-perturbative effects in M-theory on orientifolds
• Hanany-Witten Transition in Quantum Curves
• Fermi gas approach to general rank theories and quantum curves
• Non-toric Cones and Chern-Simons Quivers
• SU(N) q-Toda equations from mass deformed ABJM theory
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• 3d dualities with decoupled sectors and brane transitions
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing