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We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks overℳ  ¯    g  ,  n\overline{\mathcal{M}}_{g,n}    in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interiorℳ   g  ,  n{\mathcal{M}}_{g,n}    and the projective flatness of the Hitchin connection.

The Chern character of the Verlinde bundle over ℳ¯ g , n