A reduced BPS index of E-strings

TL;DR

This paper introduces a reduced BPS index for E-strings under a specific symmetry-breaking twist, providing a new trigonometric generalization of the Nekrasov partition function and enabling high-order genus expansion calculations.

Contribution

It presents a novel reduced BPS index for E-strings that generalizes the Nekrasov partition function and facilitates efficient computation of the genus expansion.

Findings

Derived the perturbative part of the index.

Computed initial unrefined instanton corrections.

Determined the unrefined elliptic genus of four 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.