E-strings and \(N=4\) topological Yang-Mills theories

DOI10.1016/S0550-3213(98)00426-XzbMATH Open0951.81025arXivhep-th/9802168MaRDI QIDQ1570551

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Publication date: 11 July 2000

Published in: (Search for Journal in Brave)

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 $c=12n-4-248novern+30$, 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 $halfK3$. 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 $halfK3$. 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.

Full work available at URL: https://arxiv.org/abs/hep-th/9802168

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