Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling

Abstract

Superconformal five dimensional theories have a rich structure of phases and brane webs play a crucial role in studying their properties. This paper is devoted to the study of a three parameter family of SQCD theories, given by the number of colors $N_c$ for an $SU(N_c)$ gauge theory, number of fundamental flavors $N_f$, and the Chern Simons level $k$. The study of their infinite coupling Higgs branch is a long standing problem and reveals a rich pattern of moduli spaces, depending on the 3 values in a critical way. For a generic choice of the parameters we find a surprising number of 3 different components, with intersections that are closures of height 2 nilpotent orbits of the flavor symmetry. This is in contrast to previous studies where except for one case ($N_c=2,N_f=2$), the parameters were restricted to the cases of Higgs branches that have only one component. The new feature is achieved thanks to a concept in tropical geometry which is called stable intersection and allows for a computation of the Higgs branch to almost all the cases which were previously unknown for this three parameter family apart form certain small number of exceptional theories with low rank gauge group. A crucial feature in the construction of the Higgs branch is the notion of dressed monopole operators.

arXiv comment49 pages

References in corpus (26)

• Mirror Symmetry in Three Dimensional Gauge Theories
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Branes, Superpotentials and Superconformal Fixed Points
• Webs of five-branes and N=2 superconformal field theories
• Symplectic singularities
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• General Argyres-Douglas Theory
• On Geometric Classification of 5d SCFTs
• Five-branes, Seven-branes and Five-dimensional E_n field theories
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Fractional Branes and Dynamical Supersymmetry Breaking
• Non-Lagrangian Theories from Brane Junctions
• Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
• Coulomb Branch and The Moduli Space of Instantons
• Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories
• A new 5d description of 6d D-type minimal conformal matter
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Quiver Subtractions
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Lifting 4d dualities to 5d
• Dualities and 5-brane webs for 5d rank 2 SCFTs
• Hilbert Series for Moduli Spaces of Two Instantons
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• String Junction Transitions in the Moduli Space of N=2 SYM

Cited by in corpus (60)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Lecture Notes on Generalized Symmetries and Applications
• Trifectas for $T_N$ in 5d
• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• Magnetic quivers for rank 1 theories
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• (5d RG-flow) Trees in the Tropical Rain Forest
• Classification of 5d N=1 gauge theories
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Magnetic Quivers from Brane Webs with O5 Planes
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
• Brane Webs and Magnetic Quivers for SQCD
• S-fold magnetic quivers
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study
• Magnetic Lattices for Orthosymplectic Quivers
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers
• Magnetic quivers for rank 2 theories
• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• Fibrations and Hasse diagrams for 6d SCFTs
• Folding Orthosymplectic Quivers
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Higgs Branches of U/SU Quivers via Brane Locking
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• The Hasse Diagram of the Moduli Space of Instantons
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Higgs branch RG-flows via Decay and Fission
• Higgs, Coulomb, and Hall-Littlewood
• AdS${}_6$/CFT${}_5$ with O7-planes
• Decay and Fission of Magnetic Quivers
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Discrete gauging and Hasse diagrams
• The Cat's Cradle: Deforming the higher rank $E_1$ and ${\tilde{E}}_1$ theories
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• Exploring the orthosymplectic zoo
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• On non-supersymmetric fixed points in five dimensions
• Fibre-base duality of 5d KK theories
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• Atomic Higgsings of 6D SCFTs
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• Poisson Brackets for some Coulomb Branches
• 5d SCFTs and their non-supersymmetric cousins
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
• Magnetic quivers from brane webs with O7${}^{+}$-planes
• FI-flows of 3d N=4 Theories