E + E $\rightarrow$ H

TL;DR

This paper derives explicit formulas for the elliptic genus of two E-strings using string dualities and demonstrates how to recover the elliptic genus of heterotic strings, revealing deep mathematical identities among Jacobi forms.

Contribution

It provides the first explicit expressions for the elliptic genus of two E-strings and connects them to heterotic strings via M-theory dualities, uncovering new mathematical identities.

Findings

Explicit elliptic genus expressions for two E-strings.

Recovery of heterotic string elliptic genus from E-string data.

Discovery of non-trivial identities among Jacobi forms.

Abstract

E-strings arise from M2 branes suspended between an M5 brane and an M9 plane. In this paper we obtain explicit expressions for the elliptic genus of two E-strings using a series of string dualities. Moreover we show how this can be used to recover the elliptic genus of two $E_8\times E_8$ heterotic strings using the Horava-Witten realization of heterotic strings in M-theory. This involves highly non-trivial identities among Jacobi forms, and is remarkable in light of the fact that E-strings are 'sticky' and form bound states whereas heterotic strings do not form bound states.