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 (hp,q ≠ 0,p ≠ q) and suggest that the Virasoro condition holds universally for all compact smooth Kähler manifolds.
- Quantum cohomology
- Topological field theory
- Virasoro algebra
ASJC Scopus subject areas
- Nuclear and High Energy Physics