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Abstract: We propose a new, conjectural recursion solution for Hurwitz numbers at allgenera. This conjecture is based on recent progress in solving type Btopological string theory on the mirrors of toric Calabi-Yau manifolds, whichwe briefly review to provide some background for our conjecture. We show inparticular how this B-model solution, combined with mirror symmetry for theone-leg, framed topological vertex, leads to a recursion relation for Hodgeintegrals with three Hodge class insertions. Our conjecture in Hurwitz theoryfollows from this recursion for the framed vertex in the limit of infiniteframing.



Autor: Vincent Bouchard, Marcos Marino

Fuente: https://arxiv.org/







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