Quantum cohomology and free field representation
Sep, 1997
13 pages
Published in:
- Nucl.Phys.B 510 (1998) 608-622
e-Print:
- hep-th/9709152 [hep-th]
Report number:
- UT-789,
- YITP-97-47
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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 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 () and suggest that the Virasoro condition holds universally for all compact smooth K\"{a}hler manifolds.- 11.25.Hf
- 11.10.Kk
- 11.15.Tk
- Quantum cohomology
- Topological field theory
- Virasoro algebra
- field theory: conformal
- dimension: 2
- operator: Virasoro
- operator: algebra
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