Quantum Cohomology and Free Field Representation

Details Quantum Cohomology and Free Field Representation Quantum Cohomology and Free Field Representation

1997-09-20

arxiv.org/abs/hep-th/9709152v1

Nucl.Phys. B510 (1998) 608-622

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 13pages

Scientific paper

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 K\"{a}hler 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 K\"{a}hler manifolds.

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