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Partition Functions for BPS States of the Non-Critical E₈ String
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Partition Functions for BPS States of the Non-Critical E₈ String
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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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Cited by 1 Pith paper
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BPS Invariants for Generalized Toric Calabi-Yau Threefolds
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