Partition functions for BPS states of the non-critical \(E_8\) string. (English) Zbl 0898.32013
There are found explicit expressions (in terms of modular forms) for the momentum partition functions \(G_n\) for the states with winding number \(n\) by considering the BPS states of the \(E_8\) non-critical string wound around one of the circles of a toroidal compactification to four dimensions. It is formulated an algorithm for generating the \(G_n\) by proving a recurrence relation being reminiscent of the holomorphic anomaly equations of Kodaira-Spencer theory.
Reviewer: Sergiu I.Vacaru (Chişinǎu)
MSC:
32G81 | Applications of deformations of analytic structures to the sciences |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
14J28 | \(K3\) surfaces and Enriques surfaces |