Discrete Gauging in Six Dimensions

Abstract

When $n$ M5 branes coincide on an A type singularity, ${\mathbb{C}}^2/{\mathbb{Z}}_k$, there is a multitude of tensionless strings which arise in the spectrum. The low energy theory when all M5 branes are separated at the singularity is given by a linear quiver with parameters $n$ and $k$. The theory has a multitude of phases, as many as partitions of $n$, each characterized by a different Higgs branch. Each such Higgs branch can be described by a Coulomb branch of a 3d $\mathcal{N}=4$ quiver. For example, at finite coupling, when all branes are separated, the quiver has a bouquet of $n$ $U(1)$ nodes connected to a single node. There is a natural discrete non Abelian $S_n$ global symmetry which acts in the theory by permuting $n$ identical objects. It acts in particular on the Higgs branch at the above finite coupling phase. It is conjectured that at the coincident point this discrete $S_n$ flavor symmetry is gauged, and at partial coincidence the corresponding subgroup of $S_n$ is gauged. This elegant and simple effect solves several problems which are raised recently on the physics of multiple M5 branes on an A type singularity. Similar results on multitude of phases are concluded for a system of $n$ M5 branes on an A type singularity next to an M9 plane.

32 pages, 3 figures

References in corpus (12)

• 6d Conformal Matter
• Webs of five-branes and N=2 superconformal field theories
• Mirrors of 3d Sicilian theories
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Branes and the Kraft-Procesi Transition
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Highest Weight Generating Functions for Hilbert Series
• Tri-vertices and SU(2)'s
• Branes and the Kraft-Procesi transition: classical case
• Complete Graphs, Hilbert Series, and the Higgs branch of the 4d N=2 $(A_n,A_m)$ SCFT's
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras

Cited by in corpus (48)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Universal Features of BPS Strings in Six-dimensional SCFTs
• 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
• Compactifications of ADE conformal matter on a torus
• Magnetic Quivers from Brane Webs with O5 Planes
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Revisiting the classifications of 6d SCFTs and LSTs
• Brane Webs and Magnetic Quivers for SQCD
• S-fold magnetic quivers
• Magnetic Lattices for Orthosymplectic Quivers
• From 6d flows to 4d flows
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• General Prescription for Global U(1)'s in 6D SCFTs
• Discrete gauge theories of charge conjugation
• 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
• Discrete Gauging in Coulomb branches of Three Dimensional $\mathcal{N}=4$ Supersymmetric Gauge Theories
• Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index
• Charges and holography in 6d (1,0) theories
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Magnetic quivers and negatively charged branes
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• The moduli spaces of S-fold CFTs
• Coulomb Branch Global Symmetry and Quiver Addition
• Curious patterns of IR symmetry enhancement
• Higgs, Coulomb, and Hall-Littlewood
• On the torus compactifications of $Z_2$ orbifolds of E-string theories
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Discrete gauging and Hasse diagrams
• Symmetry enhancement in 4d Spin(n) gauge theories and compactification from 6d
• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• The Higgs branch of Heterotic ALE instantons
• Flavor symmetries of six-dimensional $\mathcal{N}=(1,0)$ theories from AdS/CFT correspondence
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Minimally Unbalanced Quivers
• Orthosymplectic Quotient Quiver Subtraction
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Atomic Higgsings of 6D SCFTs
• Some Open Questions in Quiver Gauge Theory
• Quiver Polymerisation