2017/03/31 by Chiung Hwang, Piljin Yi, Yutaka Yoshida · 26 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Duality (order theory) #Gauge theory #Invariant (physics) #Mathematical physics #Mathematics #Mechanics #Partition (number theory) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quiver #Seiberg duality #Supersymmetric gauge theory #Vortex #hep-th
paper · pdf · doi:10.1007/jhep05(2017)099
published in Journal of High Energy Physics 2017(5) (Springer Nature) · 75 pages, 24 figures; v2: a reference added, published version
openalex publication_date 2017/05/01 · arxiv created 2017/05/25 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; although the vortex number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular, where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such extra chiral fields. As such, 1d wall-crossing of the vortex theory encodes the particle-vortex duality embedded in the 3d Seiberg-like duality. For N = 4, the D-brane picture is used to motivate this 3d/1d connection, while, for N = 2, this 3d/1d connection is used to fine-tune otherwise ambiguous vortex dynamics. We also prove some identities of 3d supersymmetric partition functions for the Aharony duality using this vortex wall-crossing interpretation.