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

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

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

Authors

Minahan, J. A.

Nemeschansky, D.

Warner, N. P.

Description

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)