2014/02/20 by Anindya Dey, Amihay Hanany, Peter Koroteev +1
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Dual polyhedron #Gauge theory #Mirror symmetry #Partition function (quantum field theory) #Quantum Chromodynamics and Particle Interactions #Quiver #Rank (graph theory) #Supersymmetric gauge theory #Symmetry (geometry) #Symplectic geometry #hep-th #math-ph #math.MP #math.RT
paper · pdf · doi:10.1007/jhep06(2014)059
published as JHEP06 (2014) 059 · 73 pages, many figures, typos corrected
arxiv created 2014/02/20 · openalex publication_date 2014/06/01 · arxiv updated 2014/07/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Starting from mirror pairs consisting only of linear (framed A-type) quivers, we demonstrate that a wide class of three-dimensional quiver gauge theories with N = 4 supersymmetry and their mirror duals can be obtained by suitably gauging flavor symmetries. Infinite families of mirror pairs including various quivers of D and E-type and their affine extensions, star-shaped quivers, and quivers with symplectic gauge groups may be generated in this fashion. We present two different computational strategies to perform the aforementioned gauging procedure — one of them involves N = 2* classical parameter space description, while the other one uses partition functions of the N = 4 theories on S 3. The partition function, in particular, turns out to be an extremely efficient tool for implementing this gauging procedure as it readily generalizes to arbitrary size of the quiver and arbitrary rank of the gauge group at each node. For most examples of mirror pairs obtained via this procedure, we perform additional checks of mirror symmetry using the Hilbert series.