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arXiv · 2406.07459

Hodge structures on conformal blocks

Pierre Godfard
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Abstract

We prove existence and uniqueness of complex Hodge structures on modular functors. The proof is based on the non-Abelian Hodge correspondence and Ocneanu rigidity. Given a modular functor, we explain how its Hodge numbers fit into a Frobenius algebra and the Chern characters of its Hodge decompositions into a new cohomological field theory (CohFT). In the case of $\mathrm{SU}(2)$ modular functors of level $2$ times an odd number, we give explicit formulas for all Hodge numbers, in any genus $g$.

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Pierre Godfard. 2025-07-10. Hodge structures on conformal blocks. https://arxiv.org/abs/2406.07459

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