Elliptic Genus of E-strings

Abstract

We study a family of 2d N=(0,4) gauge theories which describes at low energy the dynamics of E-strings, the M2-branes suspended between a pair of M5 and M9 branes. The gauge theory is engineered using a duality with type IIA theory, leading to the D2-branes suspended between an NS5-brane and 8 D8-branes on an O8-plane. We compute the elliptic genus of this family of theories, and find agreement with the known results for single and two E-strings. The partition function can in principle be computed for arbitrary number of E-strings, and we compute them explicitly for low numbers. We test our predictions against the partially known results from topological strings, as well as from the instanton calculus of 5d Sp(1) gauge theory. Given the relation to topological strings, our computation provides the all genus partition function of the refined topological strings on the canonical bundle over 1/2 K3.

49 pages, 2 figures

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• 6d Conformal Matter
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• Holography for (1,0) theories in six dimensions
• The Holographic Dual of AdS3 x S3 x S3 x S1
• Instantons on the 5-sphere and M5-branes
• Superconformal Partition Functions and Non-perturbative Topological Strings
• E + E $\to$ H
• Factorization of 5D super Yang-Mills on $Y^{p,q}$ spaces
• Gluing Nekrasov partition functions
• Higgsing towards E-strings
• A reduced BPS index of E-strings

Cited by in corpus (64)

• Strings of Minimal 6d SCFTs
• F-Theory, Spinning Black Holes and Multi-string Branches
• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Tao Probing the End of the World
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Surface Defect, Anomalies and $b$-Extremization
• AdS${}_7$/CFT${}_6$ with orientifolds
• Little strings and T-duality
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Bootstrapping BPS spectra of 5d/6d field theories
• Blowup Equations for Refined Topological Strings
• 6d strings from new chiral gauge theories
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Topological vertex formalism with O5-plane
• On elliptic genera of 6d string theories
• Dual Little Strings and their Partition Functions
• 6d strings and exceptional instantons
• Real ADE-equivariant (co)homotopy and Super M-branes
• Supersymmetric index on T^2 x S^2 and elliptic genus
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups
• 5d/6d Wilson loops from blowups
• D-type fiber-base duality
• General instanton counting and 5d SCFT
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• E-string Quantum Curve
• Little strings on $D_n$ orbifolds
• M5 branes and Theta Functions
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• 2d small N=4 Long-multiplet superconformal block
• Topological vertex for 6d SCFTs with ${\mathbb{Z}}_2$-twist
• Surface defects on E-string from 5-brane webs
• Refined topological vertex with ON-planes
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Topological strings and Wilson loops
• Higgsing towards E-strings
• Cardy Limits of 6d Superconformal Theories
• Seiberg-like dualities for orthogonal and symplectic 3d $\mathcal{N}=2$ gauge theories with boundaries
• S-foldings of 5d SCFTs
• Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories
• Blowup Equations for Little Strings
• Asymptotic M5-brane entropy from S-duality
• Towards Refining the Topological Strings on Compact Calabi-Yau 3-folds
• $DE$-type little strings from glued brane webs
• SCFTs, Holography, and Topological Strings
• Transitions of Orbifold Vacua
• A Lagrangian for self-dual strings
• M-strings in thermodynamic limit: Seiberg-Witten geometry
• Bootstrapping ADE M-strings
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Proving the 6d Cardy Formula and Matching Global Gravitational Anomalies
• E-strings, $F_4$, and $D_4$ triality
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Affine characters at negative level and elliptic genera of non-critical strings
• 2d duality for orthogonal gauge theories with 8 supersymmetries
• Elliptic Genus, Anomaly Cancellation and Heterotic M-theory
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• 2D Seiberg-like dualities for orthogonal gauge groups
• Topological String on elliptic CY 3-folds and the ring of Jacobi forms
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Recent Developments in Topological String Theory
• Heterotic M2-branes