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arXiv · hep-th/9703086

Quantum Cohomology and Virasoro Algebra

Tohru Eguchi·Kentaro Hori·Chuan-Sheng Xiong
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Abstract

We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds $M$ ($c_1(M)>0$) and determines their partition functions at all genera. We construct Virasoro operators in the case of complex projective spaces and show that they reproduce the results of Kontsevich-Manin, Getzler etc. on the genus-0,1 instanton numbers. We also construct Virasoro operators for a wider class of Fano varieties. The central charge of the algebra is equal to $χ(M)$, the Euler characteristic of the manifold $M$.

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Tohru Eguchi, Kentaro Hori, Chuan-Sheng Xiong. 1997-04-20. Quantum Cohomology and Virasoro Algebra. https://doi.org/10.1016/s0370-2693(97)00401-2

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