Atomic Higgsings of 6D SCFTs

Abstract

In this paper, we study the full Higgs branch Hasse diagram for any given 6d $\mathcal{N}=(1,0)$ SCFT constructed via F-theory. This can be done by a procedure of determining all the minimal Higgsings on the generalized quiver of the 6d SCFT. We call this procedure the atomic Higgsing, which can be implemented iteratively. We present our general algorithms with many concrete examples of Hasse diagrams. We also compare our algorithm with the Higgsings determined by the 3d $\mathcal{N}=4$ magnetic quivers. For the cases where the magnetic quivers are unitary, we can reproduce the full Hasse diagrams. We also construct the orthosymplectic magnetic quivers from the Type IIA brane systems for some new examples. Our approach, based on F-theory, applies to the known and new orthosymplectic cases, as well as theories that do not have known descriptions in terms of magnetic quivers. We expect our geometry-based approach to help extend the horizon of the RG flows of the 6d SCFTs.

75 pages and appendices. v2: references add, minor corrections

References in corpus (79)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Five-Brane Effective Action In M-Theory
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Branes and Six Dimensional Supersymmetric Theories
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Matter From Geometry
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• T-Branes and Monodromy
• Anomaly polynomial of general 6d SCFTs
• Non-abelian Tensor-multiplet Anomalies
• On renormalization group flows and the a-theorem in 6d
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Top Down Approach to 6D SCFTs
• Issues on Orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
• Coulomb Branch and The Moduli Space of Instantons
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• T-Branes and Geometry
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Anomaly polynomial of E-string theories
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Quiver Subtractions
• 6D RG Flows and Nilpotent Hierarchies
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Branes and the Kraft-Procesi Transition
• Discrete Gauging in Six Dimensions
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
• (5d RG-flow) Trees in the Tropical Rain Forest
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• Mirror symmetry by O3-planes
• Magnetic Quivers from Brane Webs with O5 Planes
• Fission, Fusion, and 6D RG Flows
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• Branes and the Kraft-Procesi transition: classical case
• T-branes, Anomalies and Moduli Spaces in 6D SCFTs
• Small instanton transitions for M5 fractions
• Magnetic Lattices for Orthosymplectic Quivers
• General Prescription for Global U(1)'s in 6D SCFTs
• T-Branes, String Junctions, and 6D SCFTs
• Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Coulomb branches of quiver gauge theories with symmetrizers
• On the global symmetries of 6D superconformal field theories
• Fibrations and Hasse diagrams for 6d SCFTs
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Quiver origami: discrete gauging and folding
• Discrete Gauging in Coulomb branches of Three Dimensional $\mathcal{N}=4$ Supersymmetric Gauge Theories
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index
• The Hasse Diagram of the Moduli Space of Instantons
• Magnetic quivers and negatively charged branes
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Higgs branch RG-flows via Decay and Fission
• Quiver Theories and Formulae for Slodowy Slices of Classical Algebras
• Decay and Fission of Magnetic Quivers
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• The Higgs branch of Heterotic ALE instantons
• Exploring the orthosymplectic zoo
• Line bundles over Coulomb branches
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• 6d/5d exceptional gauge theories from web diagrams
• Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
• Orthosymplectic Quotient Quiver Subtraction
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Nilpotent orbit Coulomb branches of types AD
• Introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories
• Atomic Higgsings of 6D SCFTs II: Induced Flows

Cited by in corpus (2)

• Atomic Higgsings of 6D SCFTs II: Induced Flows
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D