Fusing E-strings to heterotic strings:E+E→H

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 × E 8 heterotic strings using the Hořava-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.

Elliptic genus of E-strings

“…Explicit computations for the elliptic genus are now straightforward, but somewhat cumbersome. Nevertheless we carry it out explicitly for the case of n E-strings for n = 1, 2, 3, 4, and also explain the concrete procedures needed to compute the elliptic genus in the case with general n. The case with n = 1 was already known in [19], and the case with n = 2 was recently found in [7]. For the other two cases we check our results against partial results from topological strings on 1 2 K3 (where low genus answer is known).…”

“…This was done by constraining its form with its modularity, the 'domain wall' ansatz of [5], and a few low order coefficients in the genus expansion known from the topological string calculus. The result of [7] is given by…”

“…They are rather enigmatic as they include tensionless self-dual strings as their building blocks. The study of these theories has recently intensified, leading to computations of their superconformal indices [1][2][3][4], the elliptic genera of the self-dual strings in the Coulomb branch [5][6][7] (see [8] for an earlier work), as well as a partial classification of 6d superconformal theories [9][10][11]. The aim of this paper is to take a step forward in this direction, in particular focusing on one of the most basic (1, 0) superconformal theories.…”

From strings in 6d to strings in 5d

“…However, as argued in [5], one has to add to the above expression the following term 13) which is due to moving infinitesimally away from the boundary of the Kähler cone (4.6), in order to arrive in the weak coupling chamber of the field theory. Expanding the sum of (4.12) and (4.13) in powers of Q τ we can again obtain Betti numbers.…”

“…The six-dimensional parent theory has itself strings and in a compactification to five dimensions they may or may not wrap the circle. In case they do wrap the circle their elliptic genus can be computed through various techniques which have recently been developed [11][12][13][14] and allow to obtain the partition function of the six-dimensional theory on T 2 × R 4 :…”