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Two Proofs of a Conjecture of Hori and Vafa

Aaron Bertram·Ionut Ciocan-Fontanine·Bumsig Kim
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Abstract

We give two proofs of a conjecture of Hori and Vafa which expresses the J-function (i.e, the generating function for 1-point descendant Gromov-Witten invariants) of a Grassmannian in terms of the J-function of a product of projective spaces. Similar relations are obtained for two-point descendants, and three-point (primary) Gromov-Witten invariants. As an application we prove Givental's "R-Conjecture" - hence the Virasoro conjecture - for Grassmannians.

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Aaron Bertram, Ionut Ciocan-Fontanine, Bumsig Kim. 2003-04-25. Two Proofs of a Conjecture of Hori and Vafa. https://arxiv.org/abs/math/0304403

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