The Knizhnik-Zamolodchikov and Hitchin connections are projectively equivalent in genus zero via Pauly's isomorphism, yielding a projectively unique and flat Hitchin connection from a metaplectic correction.
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The Hitchin and Knizhnik-Zamolodchikov connections are projectively equivalent in the genus zero case
The Knizhnik-Zamolodchikov and Hitchin connections are projectively equivalent in genus zero via Pauly's isomorphism, yielding a projectively unique and flat Hitchin connection from a metaplectic correction.