Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch

Abstract

We study the stratification of the singular locus of four dimensional $\mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed -- the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata -- are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed "elementary slices" is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.

arXiv comment64 pages, 27 figures, submitted to JHEP

References in corpus (35)

• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• F-theory and Orientifolds
• Reading between the lines of four-dimensional gauge theories
• New N=2 Superconformal Field Theories in Four Dimensions
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Superconformal Fixed Points with E_n Global Symmetry
• F-Theory at Constant Coupling
• Probing F-theory With Branes
• General Argyres-Douglas Theory
• Central charges of N=2 superconformal field theories in four dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• S-folds and 4d N=3 superconformal field theories
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Tinkertoys for the Twisted D-Series
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• Branes and the Kraft-Procesi Transition
• Magnetic quivers for rank 1 theories
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• 4d $\mathcal{N}=2$ S-folds
• Branes and the Kraft-Procesi transition: classical case
• Revisiting the classifications of 6d SCFTs and LSTs
• Brane Webs and Magnetic Quivers for SQCD
• Gauge theories from principally extended disconnected gauge groups
• Free Field Realizations from the Higgs Branch
• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• VOAs and rank-two instanton SCFTs
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• Coulomb branches with complex singularities
• Weakly coupled conformal manifolds in 4d
• Compactifications of 5d SCFTs with a twist

Cited by in corpus (20)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• S-fold magnetic quivers
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• New N=2 superconformal field theories from S-folds
• Magnetic quivers for rank 2 theories
• Fibrations and Hasse diagrams for 6d SCFTs
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• On the compactification of 5d theories to 4d
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• A new rank-2 Argyres-Douglas theory
• Multiple phases and meromorphic deformations of unitary matrix models
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Disconnected gauge groups in the infrared
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial