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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 E8×E8 heterotic strings using the Hořava-Witten realization of heterotic strings in M-theory. This involves highly nontrivial 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. [ABSTRACT FROM AUTHOR]

We consider M theory in the presence of M parallel M5-branes probing a transverse AN-1 singularity. This leads to a superconformai theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of this theory on a two-torus, with arbitrary supersymmetry preserving twists, using the topological vertex formalism. Alternatively, we show that this can also be obtained by computing the elliptic genus of an orbifold of recently studied M-strings. The resulting two-dimensional theory is a (4,0) supersymmetric quiver gauge theory whose Higgs branch corresponds to strings propagating on the moduli space of SU(N)M-1 instantons on R4, where the right-moving fermions are coupled to a particular bundle. [ABSTRACT FROM AUTHOR]