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

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

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arXiv · hep-th/9707149

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

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

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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.

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J. A. Minahan, D. Nemeschansky, N. P. Warner. 1997-07-16. Partition Functions for BPS States of the Non-Critical E_8 String. https://arxiv.org/abs/hep-th/9707149

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