Exact Gravitational Threshold Correction in the FHSV Model
Abstract
We consider the automorphic forms which govern the gravitational threshold correction F1 in models of heterotic/IIA duality with N=2 supersymmetry in four dimensions. In particular we derive the full nonperturbative formula for F1 for the dual pair originally considered by Ferrara, Harvey, Strominger and Vafa (FHSV). The answer involves an interesting automorphic product constructed by Borcherds which is associated to the ``fake Monster Lie superalgebra.'' As an application of this result we rederive a result of Jorgenson & Todorov on determinants of ∂ operators on K3 surfaces.
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