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We prove an explicit formula for the total Chern character of the Verlindebundle over the moduli space of pointed stable curves in terms of tautologicalclasses. The Chern characters of the Verlinde bundles define a semisimple CohFT(the ranks, given by the Verlinde formula, determine a semisimple fusionalgebra). According to Teleman's classification of semisimple CohFTs, thereexists an element of Givental's group transforming the fusion algebra into theCohFT. We determine the element using the first Chern class of the Verlindebundle on the moduli space of nonsingular curves and the projective flatness ofthe Hitchin connection.

The Chern character of the Verlinde bundle over the moduli space of stable curves