Partition Functions for BPS States of the Non-Critical E_8 String

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

paper

Partition Functions for BPS States of the Non-Critical E_8 String

arXiv:hep-th/9707149

Abstract

We consider the BPS states of the $E_{8}$ non-critical string wound around one of the circles of a toroidal compactification to four dimensions. These states are indexed by their momenta and winding numbers. We find explicit expressions, $G_{n}$ , for the momentum partition functions for the states with winding number $n$ . The $G_{n}$ are given in terms of modular forms. We give a simple algorithm for generating the $G_{n}$ , and we show that they satisfy a recurrence relation that is reminiscent of the holomorphic anomaly equations of Kodaira-Spencer theory.

17 pages, harvmac(b)

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