A reduced BPS index of E-strings

Abstract

We study the BPS spectrum of E-strings in a situation where the global E_8 symmetry is broken down to D_4 + D_4 by a certain twist. We find that the refined BPS index in this setup serves as a reduced BPS index of E-strings, which gives a novel trigonometric generalization of the Nekrasov partition function for four-dimensional N=2 supersymmetric SU(2) gauge theory with N_f=4 massless flavors. We determine the perturbative part of this index and also first few unrefined instanton corrections. By using these results together with the modular anomaly equation, the genus expansion of the free energy can be computed efficiently up to very high order. We also determine the unrefined elliptic genus of four E-strings under the twist.

23 pages, v2: typos corrected, v3: footnotes added, published version

References in corpus (21)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Comments on String Dynamics in Six Dimensions
• The Refined Topological Vertex
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory
• BPS States of Exceptional Non-Critical Strings
• Direct Integration of the Topological String
• Refined stable pair invariants for E-, M- and [p,q]-strings
• The Omega deformed B-model for rigid N=2 theories
• E-Strings and N=4 Topological Yang-Mills Theories
• Anomaly polynomial of E-string theories
• On N=2 Supersymmetric QCD with 4 Flavors
• E + E $\to$ H
• Seiberg-Witten Curve for the E-String Theory
• Topological string amplitudes for the local half K3 surface
• Seiberg-Witten prepotential for E-string theory and global symmetries
• Thermodynamic limit of the Nekrasov-type formula for E-string theory
• Seiberg-Witten prepotential for E-string theory and random partitions

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• On the Elliptic Genus of Three E-strings and Heterotic Strings
• E-strings, $F_4$, and $D_4$ triality
• BPS index and 4d N=2 superconformal field theories