Quiver Subtractions

Abstract

We study the vacuum structure of gauge theories with eight supercharges. It has been recently discovered that in the Higgs branch of $5d$ and $6d$ SQCD theories with eight supercharges, the new massless states, arising when the gauge coupling is taken to infinity, can be described in terms of Coulomb branches of $3d\mathcal{N}=4$ quiver gauge theories. The description of this new phenomenon draws from the ideas discovered in the analysis of nilpotent orbits as Higgs and Coulomb branches of $3d$ theories and promotes the Higgs mechanism known as the Kraft-Procesi transition to the status of a new operation between quivers. This is the quiver subtraction. This paper establishes this operation formally and examines some immediate consequences. One is the extension of the physical realization of Kraft-Procesi transitions from the classical to the exceptional Lie algebras. Another result is the extension from special nilpotent orbits to non-special ones. One further consequence is the analysis of the effect in $5d\mathcal{N}=1$ SQCD of integrating out a massive quark while the gauge coupling remains infinite. In general, the subtraction of quivers sheds light on the different types of singularities within the Coulomb branch and the structure of the massless states that arise at those singular points; including the nature of the new Higgs branches that open up. This allows for a systematic analysis of mixed branches of $3d\mathcal{N}=4$ quivers that do not necessarily have a simple embedding in string theory. The subtraction of two quivers is an extremely simple resource for the theoretical physicist interested in the vacuum structure of gauge theories, and yet its power is so remarkable that is bound to play a crucial role in the coming discoveries of new and exciting physics in $5$ and $6$ dimensions.

21 pages

References in corpus (17)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Mirrors of 3d Sicilian theories
• Coulomb Branch and The Moduli Space of Instantons
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Fiber-Base Duality and Global Symmetry Enhancement
• T^σ_ρ(G) Theories and Their Hilbert Series
• Duality and enhancement of symmetry in 5d gauge theories
• Branes and the Kraft-Procesi Transition
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• Branes and the Kraft-Procesi transition: classical case
• Small instanton transitions for M5 fractions
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
• A comment on the enhancement of global symmetries in superconformal SU(2) gauge theories in 5D
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• ADHM and the 4d Quantum Hall Effect

Cited by in corpus (53)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• Trifectas for $T_N$ in 5d
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• (5d RG-flow) Trees in the Tropical Rain Forest
• Magnetic Quivers from Brane Webs with O5 Planes
• (Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest
• S-fold magnetic quivers
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Magnetic Lattices for Orthosymplectic 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
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• The Hasse Diagram of the Moduli Space of Instantons
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Magnetic quivers and negatively charged branes
• Coulomb Branch Global Symmetry and Quiver Addition
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Higgs branch RG-flows via Decay and Fission
• Decay and Fission of Magnetic Quivers
• Probing 7-branes on Orbifolds
• Quiver Theories and Formulae for Slodowy Slices of Classical Algebras
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Discrete gauging and Hasse diagrams
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• The Higgs branch of Heterotic ALE instantons
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• On non-supersymmetric fixed points in five dimensions
• Minimally Unbalanced Quivers
• Orthosymplectic Quotient Quiver Subtraction
• Generalized Toric Polygons, T-branes, and 5d SCFTs
• Quotient Quiver Subtraction
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Nilpotent orbit Coulomb branches of types AD
• Atomic Higgsings of 6D SCFTs
• Complex Symplectic Contractions and 3d Mirrors
• Branes, Quivers, and the Affine Grassmannian
• Moduli space singularities for $3d$ $\mathcal{N}=4$ circular quiver gauge theories
• Some Open Questions in Quiver Gauge Theory
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• $D_n$ Dynkin quiver moduli spaces
• Quiver Polymerisation
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• FI-flows of 3d N=4 Theories
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D