Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings

Abstract

Symmetries of Seiberg-Witten (SW) geometries capture intricate physical aspects of the underlying 4d $\mathcal{N}=2$ field theories. For rank-one theories, these geometries are rational elliptic surfaces whose automorphism group is a semi-direct product between the Coulomb branch (CB) symmetries and the Mordell-Weil group. We study quotients of the SW geometry by subgroups of its automorphism group, which most naturally become gaugings of discrete 0- and 1-form symmetries. Yet, new interpretations of these surgeries become evident when considering 5d $\mathcal{N}=1$ superconformal field theories. There, certain CB symmetries are related to symmetries of the corresponding $(p,q)$-brane web and, as a result, CB surgeries can give rise to (fractional) S-folds. Another novel interpretation of these quotients is the folding across dimensions: circle compactifications of the 5d $E_{2N_f+1}$ Seiberg theories lead in the infrared to two copies of locally indistinguishable 4d SU(2) SQCD theories with $N_f$ fundamental flavours. This extends earlier results on holonomy saddles, while also reproducing detailed computations of 5d BPS spectra and predicting new 5d and 6d BPS quivers. Finally, we argue that the semi-direct product structure of the automorphism group of the SW geometry includes mixed 't Hooft anomalies between the 0- and 1-form symmetries, and we also present some new results on non-cyclic CB symmetries.

arXiv comment52 pages + appendices, 10 figures. v2: minor changes, references added

References in corpus (109)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Generalized Global Symmetries
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Geometric Engineering of Quantum Field Theories
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• F-theory and Orientifolds
• Reading between the lines of four-dimensional gauge theories
• New N=2 Superconformal Field Theories in Four Dimensions
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• D-Branes And Mirror Symmetry
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Exploring 2-Group Global Symmetries
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Superconformal Fixed Points with E_n Global Symmetry
• On 2-Group Global Symmetries and Their Anomalies
• Probing F-theory With Branes
• Issues in Topological Gauge Theory
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• M-Strings
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• On the Defect Group of a 6D SCFT
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Measuring Small Distances in N=2 Sigma Models
• E-Strings and N=4 Topological Yang-Mills Theories
• S-folds and 4d N=3 superconformal field theories
• Generalized Global Symmetries of $T[M]$ Theories. I
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Curves of Marginal Stability and Weak and Strong-Coupling BPS Spectra in $N=2$ Supersymmetric QCD
• Higher Form Symmetries and M-theory
• Instanton sums and five-dimensional gauge theories
• Infinite coupling duals of N=2 gauge theories and new rank 1 superconformal field theories
• Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves
• The BPS Spectra and Superconformal Points in Massive N=2 Supersymmetric QCD
• On Painlevé/gauge theory correspondence
• N=2 supersymmetric dynamics for pedestrians
• Brane Tilings and Reflexive Polygons
• 2-Group Symmetries and M-Theory
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• On N=2 Supersymmetric QCD with 4 Flavors
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Softly Broken N=2 QCD with Massive Quark Hypermultiplets, I
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• D-Branes on Calabi-Yau Manifolds
• 4d $\mathcal{N}=2$ S-folds
• Gauge theories from principally extended disconnected gauge groups
• Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves
• Seiberg-Witten Curve for the E-String Theory
• 5D and 6D SCFTs from ${\mathbb{C}}^3$ orbifolds
• Superconformal invariance and the geography of four-manifolds
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• Donaldson invariants for nonsimply connected manifolds
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
• Integrating over the Coulomb branch in N=2 gauge theory
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions
• Special Arithmetic of Flavor
• Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces
• On the Seiberg-Witten Approach to electric-magnetic Duality
• Holonomy Saddles and Supersymmetry
• Donaldson-Witten theory and indefinite theta functions
• Renormalization and BRST symmetry in Donaldson-Witten theory
• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Dessins d'Enfants in $\mathcal{N}=2$ Generalised Quiver Theories
• Twisted Partition Functions and $H$-Saddles
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Kummer surfaces associated with Seiberg-Witten curves
• Elliptic Loci of SU(3) Vacua
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Cutting and gluing with running couplings in $\mathcal{N}=2$ QCD
• SU(2)-Donaldson invariants of the complex projective plane
• Eta Products, BPS States and K3 Surfaces
• Four flavours, triality and bimodular forms
• Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Generalized quotients and holographic duals for 5d S-fold SCFTs
• S-foldings of 5d SCFTs
• Donaldson invariants of CP^1 x CP^1 and Mock Theta Functions
• Aspects of 5d Seiberg-Witten Theories on ${\mathbb{S}}^1$
• Moonshine and Donaldson invariants of CP^2
• Mirror Symmetry
• The signature of the Seiberg-Witten surface
• On modular forms for some noncongruence arithmetic subgroups
• The $u$-plane integral, mock modularity and enumerative geometry
• Permutations of Massive Vacua
• Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with Matter
• Disconnected gauge groups in the infrared
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• E-strings, $F_4$, and $D_4$ triality
• The rank-2 classification problem III: curves with additional automorphisms
• The rank 2 classification problem I: scale invariant geometries
• Classification of rank one 5d $\mathcal{N}=1$ and 6d $(1,0)$ SCFTs
• Four-Manifold Invariants and Donaldson-Witten Theory
• Direct and Inverse Problems in Special Geometry
• Folding transformations for q-Painleve equations
• Exceptional S-fold SCFTs are almost trivial
• Genus 2 Seiberg-Witten curves for rank 2 N=4 superYang-Mills theories

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