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 \( \mathcal{N} \) = 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.
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Sakai, K. A reduced BPS index of E-strings. J. High Energ. Phys. 2014, 47 (2014). https://doi.org/10.1007/JHEP12(2014)047
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DOI: https://doi.org/10.1007/JHEP12(2014)047