E-STRINGS AND N=4 TOPOLOGICAL YANG-MILLS THEORIES

We study certain properties of six-dimensional tensionless E-strings ( arising from zero size E-8 instantons). In particular we show that n E -strings form a bound string which carries an E-8 level-n current alge bra as well as a left-over conformal system with c = 12n - 4 - (248n/n + 30), whose characters can be computed. Moreover we show that the ch aracters of the n-string bound state are captured by N = 4 U(n) topolo gical Yang-Mills theory on 1/2K3. This relation not only illuminates c ertain aspects of E-strings but can also be used to shed light on the properties of N = 4 topological Yang-Mills theories on manifolds with b(2)(+) = 1. In particular the E-string partition functions, which can be computed using local mirror symmetry on a Calabi-Yau threefold, gi ve the Euler characteristics of the Yang-Mills instanton moduli space on 1/2K3. Moreover, the partition functions are determined by a gap co ndition combined with a simple recurrence relation which has its origi ns in a holomorphic anomaly that has been conjectured to exist for N = 4 topological Yang-Mills on manifolds with b(2)(+) = 1 and is also re lated to the holomorphic anomaly for higher genus topological strings on Calabi-Yau threefolds. (C) 1998 Published by Elsevier Science B.V.