Universal Features of BPS Strings in Six-dimensional SCFTs

Abstract

In theories with extended supersymmetry the protected observables of UV superconformal fixed points are found in a number of contexts to be encoded in the BPS solitons along an IR Coulomb-like phase. For six-dimensional SCFTs such a role is played by the BPS strings on the tensorial Coulomb branch. In this paper we develop a uniform description of the worldsheet theories of a BPS string for rank-one 6d SCFTs. These strings are the basic constituents of the BPS string spectrum of arbitrary rank six-dimensional models, which they generate by forming bound states. Motivated by geometric engineering in F-theory, we describe the worldsheet theories of the BPS strings in terms of topologically twisted 4d $\mathcal{N}=2$ theories in the presence of $1/2$-BPS 2d $(0,4)$ defects. As the superconformal point of a 6d theory with gauge group $G$ is approached, the resulting worldsheet theory flows to an $\mathcal{N}=(0,4)$ NLSM with target the moduli space of one $G$ instanton, together with a nontrivial left moving bundle characterized by the matter content of the six-dimensional model. We compute the anomaly polynomial and central charges of the NLSM, and argue that the 6d flavor symmetry $F$ is realized as a current algebra on the string, whose level we compute. We find evidence that for generic theories the $G$ dependence is captured at the level of the elliptic genus by characters of an affine Kac-Moody algebra at negative level, which we interpret as a subsector of the chiral algebra of the BPS string worldsheet theory. We also find evidence for a spectral flow relating the R-R and NS-R elliptic genera. These properties of the string CFTs lead to constraints on their spectra, which in combination with modularity allow us to determine the elliptic genera of a vast number of string CFTs, leading also to novel results for 6d and 5d instanton partition functions.

arXiv comment199+1 pages; v3: references added, some typos corrected; version to appear on JHEP

References in corpus (161)

• Evidence for F-Theory
• N=2 dualities
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• Geometric Singularities and Enhanced Gauge Symmetries
• Infinite Chiral Symmetry in Four Dimensions
• D-Branes and Topological Field Theories
• Comments on String Dynamics in Six Dimensions
• A Note on the Green - Schwarz Mechanism in Open - String Theories
• Rigid Supersymmetric Theories in Curved Superspace
• The Refined Topological Vertex
• Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• Elliptic genera of 2d N=2 gauge theories
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• A topologically twisted index for three-dimensional supersymmetric theories
• Webs of five-branes and N=2 superconformal field theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Superconformal Fixed Points with E_n Global Symmetry
• Branes and Six Dimensional Supersymmetric Theories
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Probing F-theory With Branes
• The Large N Limit of $\mathcal{N}=2,1$ Field Theories from Threebranes in F-theory
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• All AdS_7 solutions of type II supergravity
• Small Instantons, del Pezzo Surfaces and Type I' theory
• Matter From Geometry
• M-Strings
• The Geometry of Supersymmetric Partition Functions
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Anomaly polynomial of general 6d SCFTs
• BPS States of Exceptional Non-Critical Strings
• W Symmetry in six dimensions
• Matrix Models, Geometric Engineering and Elliptic Genera
• Exploring Curved Superspace
• On the Defect Group of a 6D SCFT
• Classifying bases for 6D F-theory models
• Anomaly Cancellation in Six Dimensions
• Deformations of Superconformal Theories
• Holography for (1,0) theories in six dimensions
• On The Conformal Field Theory Of The Higgs Branch
• The Hilbert Series of the One Instanton Moduli Space
• Sigma Models And The ADHM Construction Of Instantons
• Tate's algorithm and F-theory
• Large N Superconformal Gauge Theories and Supergravity Orientifolds
• Generalized Green-Schwarz mechanism in F theory
• E-Strings and N=4 Topological Yang-Mills Theories
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• 6D SCFTs and Phases of 5D Theories
• Chiral algebras of class S
• On orbifolds of M-Strings
• Strings of Minimal 6d SCFTs
• More on the N=2 superconformal systems of type $D_p(G)$
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• Probing F-theory With Multiple Branes
• Topological strings and 5d T_N partition functions
• Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories
• F-theory and the Classification of Little Strings
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• Surface Defects and Chiral Algebras
• 6d holographic anomaly match as a continuum limit
• On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4
• Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity
• Infinitely many N=2 SCFT with ADE flavor symmetry
• Elliptic Genus of E-strings
• F-Theory, Spinning Black Holes and Multi-string Branches
• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• 6D RG Flows and Nilpotent Hierarchies
• F-theory and AdS_3/CFT_2
• E-String Theory on Riemann Surfaces
• The ABCDEFG of Instantons and W-algebras
• Chiral Algebras for Trinion Theories
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• D-type Conformal Matter and SU/USp Quivers
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• Anomaly Inflow for Gauge Defects
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Exploring Curved Superspace (II)
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• $(0,4)$ dualities
• Hilbert Series for Moduli Spaces of Two Instantons
• Discrete Gauging in Six Dimensions
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• M-strings, Elliptic Genera and N=4 String Amplitudes
• 5d/6d DE instantons from trivalent gluing of web diagrams
• On Arnold's 14 `exceptional' N=2 superconformal gauge theories
• On the reduction of 4d N=1 theories on S^2
• 6D Fractional Quantum Hall Effect
• Counting Exceptional Instantons
• E + E $\to$ H
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Supersymmetric AdS_7 backgrounds in half-maximal supergravity and marginal operators of (1,0) SCFTs
• On Exceptional Instanton Strings
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• AdS${}_7$/CFT${}_6$ with orientifolds
• Chiral 2d Theories from N=4 SYM with Varying Coupling
• T-branes, Anomalies and Moduli Spaces in 6D SCFTs
• $S^1/T^2$ Compactifications of 6d $\mathcal{N}=(1,0)$ Theories and Brane Webs
• Topological duality twist and brane instantons in F-theory
• F-Theory and N=1 SCFTs in Four Dimensions
• Equivalence of several descriptions for 6d SCFT
• Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory
• Little strings and T-duality
• F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter
• Small instanton transitions for M5 fractions
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• A "Lagrangian" for the E7 Superconformal Theory
• M String, Monopole String and Modular Forms
• 6d surface defects from massive type IIA
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• Notes on Supersymmetric Gauge Theories in Five and Six Dimensions
• Triality in Little String Theories
• Surface Defect Indices and 2d-4d BPS States
• An elliptic Virasoro symmetry in 6d
• From 6D SCFTs to Dynamic GLSMs
• Dual Little Strings from F-Theory and Flop Transitions
• Self-Duality and Self-Similarity of Little String Orbifolds
• On the global symmetries of 6D superconformal field theories
• More Arnold's N = 2 superconformal gauge theories
• Topological vertex formalism with O5-plane
• On the 5d instanton index as a Hilbert series
• Dual Little Strings and their Partition Functions
• There and back again: A T-brane's tale
• Holography, Brane Intersections and Six-dimensional SCFTs
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Massive sigma models with (p,q) supersymmetry
• Self-dual Strings and 2D SYM
• Special Arithmetic of Flavor
• Exact Deconstruction of the 6D (2,0) Theory
• On Three-Dimensional Quiver Gauge Theories of Type B
• F-theory and Unpaired Tensors in 6D SCFTs and LSTs
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• Green-Schwarz Automorphisms and 6D SCFTs
• D-brane anomaly inflow revisited
• From strings in 6d to strings in 5d
• Bound States of Little Strings and Symmetric Orbifold CFTs
• ADE String Chains and Mirror Symmetry
• Indices for 6 dimensional superconformal field theories
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Little strings on $D_n$ orbifolds
• Testing 5d-6d dualities with fractional D-branes
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Five-Brane Webs and Highest Weight Representations
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Classifying Global Symmetries of 6D SCFTs
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings
• The Enhancement of Supersymmetry in M-strings
• Dyonic Anomalies

Cited by in corpus (46)

• Tensionless Strings and the Weak Gravity Conjecture
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Twisted Circle Compactifications of 6d SCFTs
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• Revisiting the classifications of 6d SCFTs and LSTs
• Surface defects in the D4 $-$ D8 brane system
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Blowup Equations for 6d SCFTs. I
• A slow review of the AGT correspondence
• Searching for surface defect CFTs within AdS${}_3$
• Chiral algebras from Ω-deformation
• Flavor Symmetry of 5d SCFTs, Part 1: General Setup
• The Asymptotic Weak Gravity Conjecture in M-theory
• Generic matter representations in 6D supergravity theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• A 2d (0,2) appetizer
• 6d strings and exceptional instantons
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Instantons from Blow-up
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Magnetic quivers and negatively charged branes
• Higgs branch RG-flows via Decay and Fission
• The Geometry of the SU(2)$\times$ G${}_2$-model
• D-type fiber-base duality
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• E-string Quantum Curve
• The Higgs branch of Heterotic ALE instantons
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• Elliptic Quantum Curves of 6d SO(N) theories
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• 6d/5d exceptional gauge theories from web diagrams
• ABCD of 't Hooft operators
• Blowup Equations for Little Strings
• Hidden exceptional symmetry in the pure spinor superstring
• Weyl invariant Jacobi forms along Higgsing trees
• Isomorphisms of 4d N=2 SCFTs from 6d
• Bootstrapping ADE M-strings
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Affine characters at negative level and elliptic genera of non-critical strings