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Quantum Cohomology and Free Field Representation

Tohru Eguchi·Masao Jinzenji·Chuan-Sheng Xiong
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Abstract

In our previous article we have proposed that the Virasoro algebra controls the quantum cohomology of Fano varieties at all genera. In this paper we construct a free field description of Virasoro operators and quantum cohomology. We shall show that to each even (odd) homology class of a Kähler manifold we have a free bosonic (fermionic) field and Virasoro operators are given by a simple bilinear form of these fields. We shall show that the Virasoro condition correctly reproduces the Gromov-Witten invariants also in the case of manifolds with non-vanishing non-analytic classes ($h^{p,q}\not=0,p\not=q$) and suggest that the Virasoro condition holds universally for all compact smooth Kähler manifolds.

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Tohru Eguchi, Masao Jinzenji, Chuan-Sheng Xiong. 1997-09-20. Quantum Cohomology and Free Field Representation. https://arxiv.org/abs/hep-th/9709152

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