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

Abstract

We prove an explicit formula for the total Chern character of the Verlinde bundle over the moduli space of pointed stable curves 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 moduli space of nonsingular curves and the projective flatness of the Hitchin connection.

References in corpus (4)

• Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$
• Tautological and non-tautological cohomology of the moduli space of curves
• The Chern classes of the Verlinde bundles
• On the tautological ring of $M_{g,n}$

Cited by in corpus (5)

• Pixton's double ramification cycle relations
• Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves
• The Chern classes of the Verlinde bundles
• On higher Chern classes of vector bundles of conformal blocks
• Strange Duality of Verlinde spaces for G_2 and F_4