Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions

Abstract

We study the matrix models calculating the sphere partition functions of 3d gauge theories with $\mathcal{N}=4$ supersymmetry and a quiver structure of a $\hat{D}$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace ($\hat{A}$) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulations of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the $\hat{A}$-quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $\hat{D}$-quiver theories.

39 pages, 8 figures

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Cited by in corpus (34)

• Instanton effects in ABJM theory with general R-charge assignments
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• Instanton Effects in Orientifold ABJM Theory
• Exact relations between M2-brane theories with and without Orientifolds
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Instanton Expansion of ABJM Partition Function
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
• Charging the Conformal Window
• Orientifolding of the ABJ Fermi gas
• $q$-Virasoro modular double and 3d partition functions
• Orthosymplectic Chern-Simons Matrix Model and Chirality Projection
• 3d mirror symmetry as a canonical transformation
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• Anomalous dimensions at large charge in d=4 O(N) theory
• On Three-Dimensional Quiver Gauge Theories of Type B
• The OPE meets semiclassics
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Variations on S-fold CFTs
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Dualities in ABJM Matrix Model from Closed String Viewpoint
• Probing non-perturbative effects in M-theory on orientifolds
• Giambelli Identity in Super Chern-Simons Matrix Model
• Hanany-Witten Transition in Quantum Curves
• Non-toric Cones and Chern-Simons Quivers
• Fermi gas approach to general rank theories and quantum curves
• SU(N) q-Toda equations from mass deformed ABJM theory
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• 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
• Deconstructing Deformed D-quivers
• The Holographic Contributions to the Sphere Free Energy
• Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas