We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a string manifold is a per-Hilbert-Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.

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• In a 2-up version as PDF or PS
• In a 1-up version as PDF or PS
• On the arxiv as 0809.3108.