Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes

Abstract

We consider compactifications of very Higgsable 6d $N=(1,0)$ SCFTs on $T^2$ with non-trivial Stiefel-Whitney classes (or equivalently 't Hooft magnetic fluxes) introduced for their flavor symmetry groups. These systems can also be studied as twisted $S^1$ compactifications of the corresponding 5d theories. We deduce various properties of the resulting 4d $N=2$ SCFTs by combining these two viewpoints. In particular, we find that all 4d rank-1 $N=2$ SCFTs with a dimension-6 Coulomb branch operator with flavor symmetry ${\mathfrak{e}}_8$, $\mathfrak{usp}(10)$, $\mathfrak{su}(4)$ and $\mathfrak{su}(3)$ can be uniformly obtained by starting from a single-tensor theory in 6d. We also have a mostly independent appendix where we propose a rule to determine the Coulomb branch dimensions of 4d $N=2$ theories obtained by $T^2$ compactifications of 6d very Higgsable theories with and without Stiefel-Whitney twist.

arXiv comment70 pages, 12 figures; v2: new short subsections 3.3 and B.3; v3: published version

References in corpus (41)

• N=2 dualities
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Webs of five-branes and N=2 superconformal field theories
• Superconformal Fixed Points with E_n Global Symmetry
• Branes and Six Dimensional Supersymmetric Theories
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Bootstrapping the superconformal index with surface defects
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• Tinkertoys for Gaiotto Duality
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• Anomaly polynomial of general 6d SCFTs
• Central charges of N=2 superconformal field theories in four dimensions
• Tinkertoys for the D_N series
• Supersymmetric Index In Four-Dimensional Gauge Theories
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Tinkertoys for the Twisted D-Series
• Exceptional Indices
• Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
• A new 5d description of 6d D-type minimal conformal matter
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• 6D RG Flows and Nilpotent Hierarchies
• E-String Theory on Riemann Surfaces
• D-type Conformal Matter and SU/USp Quivers
• Tao Probing the End of the World
• Toroidal Compactification of Heterotic 6D Non-Critical Strings Down to Four Dimensions
• Compactifications of ADE conformal matter on a torus
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• The Superconformal Index of Class S Theories of Type D
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• New ``Gauge'' Theories In Six Dimensions
• Seiberg-Witten Curve for the E-String Theory
• Seiberg-Witten Geometries Revisited
• Small instanton transitions for M5 fractions
• Tinkertoys for the E7 Theory
• Compactifications of 5d SCFTs with a twist
• Comments on the twisted punctures of $A_{\text{even}}$ class S theory

Cited by in corpus (39)

• Magnetic quivers for rank 1 theories
• Rank $Q$ E-string on a torus with flux
• 4d $\mathcal{N}=2$ S-folds
• Revisiting the classifications of 6d SCFTs and LSTs
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• S-fold magnetic quivers
• Rank-3 antisymmetric matter on 5-brane webs
• A slow review of the AGT correspondence
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• New N=2 superconformal field theories from S-folds
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Quiver origami: discrete gauging and folding
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Non-Simply-Connected Symmetries in 6D SCFTs
• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Higgs, Coulomb, and Hall-Littlewood
• Probing 7-branes on Orbifolds
• On the compactification of 5d theories to 4d
• 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 $\mathsf{S}$
• On the 3d compactifications of 5d SCFTs associated with SU(N+1) gauge theories
• Elliptic Quantum Curves of 6d SO(N) theories
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking
• 6d/5d exceptional gauge theories from web diagrams
• Orthosymplectic Quotient Quiver Subtraction
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Isomorphisms of 4d N=2 SCFTs from 6d
• Compactifying 5d superconformal field theories to 3d
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Rank $Q$ E-String on Spheres with Flux
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Aspects of 4d supersymmetric dynamics and geometry
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D