E-Strings and N=4 Topological Yang-Mills Theories

J. A. Minahan; D. Nemeschansky; C. Vafa; N. P. Warner

doi:10.1016/S0550-3213(98)00426-X

paper

E-Strings and N=4 Topological Yang-Mills Theories

arXiv:hep-th/9802168 · doi:10.1016/S0550-3213(98)00426-X

Abstract

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 algebra as well as a left-over conformal system with $c = 12 n - 4 - \frac{248 n}{n + 30}$ , whose characters can be computed. Moreover we show that the characters of the $n$ -string bound state are captured by N=4 U(n) topological Yang-Mills theory on $\half K3$. This relation not only illuminates certain 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 three-fold, give the Euler characteristics of the Yang-Mills instanton moduli space on $\half K3$. Moreover, the partition functions are determined by a gap condition combined with a simple recurrence relation which has its origins 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 related to the holomorphic anomaly for higher genus topological strings on Calabi-Yau threefolds.

49 pages, no figures, harvmac. version 2: Note added, typos removed and formula (6.15) corrected

E-Strings and N=4 Topological Yang-Mills Theories

Abstract

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