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

Understand

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.