On elliptic genera of 6d string theories

Abstract

We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects the analytic structure of instanton partition functions. Given a finite amount of initial BPS data, we completely determine the elliptic genera of 6d strings in various 6d SCFTs. We also apply our ansatz to study $\mathcal{N}=(2,0)$ and $(1,1)$ little strings as well as $\mathcal{N}=(1,0)$ heterotic little strings, for which T-duality of little string theories supplies a sufficient number of initial BPS data. The anomaly polynomials of 6d little strings are worked out, which is needed for the elliptic genera bootstrap. In some little string theories, the elliptic genera must have the extra contributions from the Coulomb branch, which correspond to the additional zero modes for the full strings. The modified ansatze for such elliptic genera are also discussed.

44 pages, 7 tables

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• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Cardy Formulae for SUSY Theories in d=4 and d=6
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• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• M5-branes, orientifolds, and S-duality

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• 6d strings and exceptional instantons
• Dualities of Corner Configurations and Supersymmetric Indices
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• 5d/6d Wilson loops from blowups
• Black Hole Entropy from Quantum Mechanics
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
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• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• Cardy Limits of 6d Superconformal Theories
• Blowup Equations for Little Strings
• Weyl invariant Jacobi forms along Higgsing trees
• $DE$-type little strings from glued brane webs
• Bootstrapping ADE M-strings
• Affine characters at negative level and elliptic genera of non-critical strings