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 (hp,q ≠ 0,p ≠ q) and suggest that the Virasoro condition holds universally for all compact smooth Kähler manifolds.
Original language | English |
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Pages (from-to) | 608-622 |
Number of pages | 15 |
Journal | Nuclear Physics B |
Volume | 510 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jan 26 1998 |
Externally published | Yes |
Keywords
- Quantum cohomology
- Topological field theory
- Virasoro algebra
ASJC Scopus subject areas
- Nuclear and High Energy Physics