Abstract
We study the Polyakov path integral for the closed N = 2 fermionic string on a genus 1 worldsheet. There are sixteen spin structures, and we identify the supermoduli and gauge-field moduli for each of these. The gauge-field moduli, when present, give rise to an integral over fermion boundary conditions. Supermoduli appear at isolated points in gauge-field moduli space, and also in some sectors where gauge-field moduli are absent. Careful account is taken of measure factors in the integration over moduli, and of conformal Killing vectors, spinors and scalars. The partition function is found to be the integral of unity over moduli space with the Weil-Petersson measure.
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