Hanany-Witten effect and SL(2,Z) dualities in matrix models

Abstract

We provide tests of dualities for three-dimensional N=4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on $S^3$. The dualities are generated by SL(2,Z) transformations and Hanany-Witten 5-brane moves. These contain mirror symmetry as well as dualities identifiying fixed points of Yang-Mills quivers and Chern-Simons theories. The partition function is given by a matrix model, that can be nicely rearranged into a sequence of factors mimicking the brane realization. Identities obeyed by these elementary factors can be used to match the partition functions of dual theories, providing tests for the full web of dualities. In particular we are able to check mirror symmetry for linear and circular quivers with gauge nodes of arbitrary ranks. Our analysis also leads to a proof of a conjectured formula evaluating the matrix models of linear quiver theories.

arXiv comment65 pages, 23 figures, v2, minor clarifications added, version published on JHEP

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• T^σ_ρ(G) Theories and Their Hilbert Series
• Holographic duals of 3d S-fold CFTs
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• Zero-form and one-form symmetries of the ABJ and related theories
• Exact relations between M2-brane theories with and without Orientifolds
• The moduli spaces of $3d$ $\mathcal{N}\ge 2$ Chern-Simons gauge theories and their Hilbert series
• Supersymmetric Indices of 3d S-fold SCFTs
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• 3d mirror symmetry as a canonical transformation
• The moduli spaces of S-fold CFTs
• Mirror theories of 3d $\mathcal{N}=2$ SQCD
• On Three-Dimensional Quiver Gauge Theories of Type B
• Rethinking mirror symmetry as a local duality on fields
• 3d Mirror Symmetry from S-duality
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Variations on S-fold CFTs
• Mixed network calculus
• Hanany-Witten Transition in Quantum Curves
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• Black hole microstates and supersymmetric localization
• Fermi gas approach to general rank theories and quantum curves
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• The Space of Vacua of 3d $\mathcal{N}=3$ Abelian Theories
• Dualities for adjoint SQCD in three dimensions and emergent symmetries
• 3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality
• Brane Transitions from Exceptional Groups
• 3d dualities with decoupled sectors and brane transitions
• Mirror Symmetry And Loop Operators
• Dualities and loops on squashed $S^3$
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories