On Exceptional Instanton Strings

Abstract

According to a recent classification of 6d (1,0) theories within F-theory there are only six "pure" 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For $G$ simply-laced, we determine the 2d $\mathcal{N}=(0,4)$ worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted $S^2$ compactification of the 4d $\mathcal{N}=2$ theories of type $H_2,D_4,E_6,E_7$ and $E_8$ (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding $T^2\times S^2$ partition functions and the Hilbert series for moduli spaces of $G$ instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one $F_4$ instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d $\mathcal{N}=2$ models.

64 pages; v3: version to appear in JHEP

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• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Revisiting the classifications of 6d SCFTs and LSTs
• 4D Gauge Theories with Conformal Matter
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Anomaly matching on the Higgs branch
• A "Lagrangian" for the E7 Superconformal Theory
• Blowup Equations for 6d SCFTs. I
• Blowup Equations for Refined Topological Strings
• On elliptic genera of 6d string theories
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• The Asymptotic Weak Gravity Conjecture in M-theory
• 6d strings and exceptional instantons
• Instantons from Blow-up
• Wilson surfaces in M5-branes
• Green-Schwarz Automorphisms and 6D SCFTs
• 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
• ADE String Chains and Mirror Symmetry
• Little strings on $D_n$ orbifolds
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• Elliptic Quantum Curves of 6d SO(N) theories
• Twisted 6d $(2,0)$ SCFTs on a Circle
• ABCD of 't Hooft operators
• 6d/5d exceptional gauge theories from web diagrams
• The Fate of Discrete 1-Form Symmetries in 6d
• Blowup Equations for Little Strings
• Asymptotic M5-brane entropy from S-duality
• Weyl invariant Jacobi forms along Higgsing trees
• Punctures and Dynamical Systems
• Bootstrapping ADE M-strings
• Affine characters at negative level and elliptic genera of non-critical strings