Exact Gravitational Threshold Correction in the FHSV Model

We consider the automorphic forms which govern the gravitational threshold correction F 1 in models of heterotic/IIA duality with N = 2 supersymmetry in four dimensions. In particular we derive the full nonperturbative formula for F 1 for the dual pair origi-nally 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 K 3 surfaces.

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