On the Elliptic Genus of Three E-strings and Heterotic Strings

TL;DR

This paper derives a precise formula for the elliptic genus of three E-strings, confirms the recombination into heterotic strings, and matches results from topological string theory and orbifold calculations, advancing understanding of string dualities.

Contribution

It provides the first exact formula for the elliptic genus of three E-strings and verifies the conjecture relating E-strings to heterotic strings through detailed computations.

Findings

The elliptic genus of three E-strings matches topological string results up to genus twelve.

The heterotic string elliptic genus from M9 domain walls aligns with orbifold formula calculations.

Confirmed the n=3 case of the conjecture that E-strings can recombine into heterotic strings.

Abstract

A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n=3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.