Quantum cohomology and free-field representation

Tohru Eguchi, Masao Jinzenji, Chuan Sheng Xiong

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)608-622
Number of pages15
JournalNuclear Physics B
Volume510
Issue number3
DOIs
Publication statusPublished - Jan 26 1998
Externally publishedYes

Keywords

  • Quantum cohomology
  • Topological field theory
  • Virasoro algebra

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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