Abstract
Abstract We calculate the supersymmetric type II string partition function in a flat background for the situation where the world-sheet is hyperelliptic. We show explicitly that the contribution to the cosmological constant from hyperelliptic world-surfaces vanishes for genus ⩽ 20. This implies, in particular, that the cosmological constant vanishes completely to two loops. Due to the decoupling of the holomorphic and antiholomorphic sectors, this conclusion holds equally well for the heterotic string.
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