Quantum cohomology and free-field representation

Tohru Eguchi, Masao Jinzenji, Chuan Sheng Xiong

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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 languageEnglish
Pages (from-to)608-622
Number of pages15
JournalNuclear Physics B
Issue number3
Publication statusPublished - Jan 26 1998
Externally publishedYes


  • Quantum cohomology
  • Topological field theory
  • Virasoro algebra

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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