CALCULATION OF GROMOV-WITTEN INVARIANTS FOR CP3, CP4AND Gr(2, 4)

Jinzenji, Masao; Sun, Yi

doi:10.1142/s0217751x96000092

Cited by 8 publications

(10 citation statements)

References 9 publications

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“…We first discuss the Virasoro generators in the case of CP N manifolds and show that the Virasoro conditions eq. (1) correctly reproduce the results on instanton numbers of projective spaces obtained by [2,3,4,5,13] using the associativity of quantum cohomology ring. We then present the general form of the Virasoro operators for a wider class of Fano varieties.…”

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confidence: 82%

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Quantum cohomology and Virasoro algebra

Eguchi¹,

Hori²,

Xiong³

1997

Physics Letters B

129

172

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We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds M (c 1 (M ) > 0) and determines their partition functions at all genera. We construct Virasoro operators in the case of complex projective spaces and show that they reproduce the results of Kontsevich-Manin, Getzler etc. on the genus-0,1 instanton numbers. We also construct Virasoro operators for a wider class of Fano varieties. The central charge of the algebra is equal to χ(M ), the Euler characteristic of the manifold M .

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supporting

confidence: 82%

“…We have tested the operators (47) in the case of Grassmannian manifold Gr(2, 4) for which genus-0 instanton data exist [5]. We found that Virasoro conditions in fact reproduce correct instanton numbers of Gr (2,4).…”

mentioning

confidence: 99%

Quantum cohomology and Virasoro algebra

Eguchi¹,

Hori²,

Xiong³

1997

Physics Letters B

129

172

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“…In such cases, identities ∂ t l κ m = ∂ t m κ l are satisfied automatically and integrable conditions are turned into formulae These determine instanton parts of prepotentials completely [12,13,14]. Under these conditions (4.…”

Section: Fusion Relations For Operatorsmentioning

confidence: 99%

“…Also it is known that the closed string amplitudes {κ m } can be calculated recursively [12,13,14] by associativity relations of operators for Fano manifolds. In our case these associativities appear naturally as integrable conditions for a set of differential equations satisfied by the …”

Section: Introductionmentioning

confidence: 99%

Disk amplitudes in the topological A-model on Calabi-Yau spaces and Fano manifolds

Sugiyama

1999

Nuclear Physics B

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“…[6,7,8,9,10]. This method is efficient and general, however, is limited to the genus g = 0 case at the moment.…”

Section: When the Target Space M Is A Calabi-yau Manifold A Special mentioning

confidence: 99%

Topological σ-models and the large-N matrix integrals

Eguchi

1996

Nuclear Physics B - Proceedings Supplements

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In this paper we describe in some detail the representation of the topological CP 1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP 1 model and show that it is governed by an extension of the 1-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP 1 . We compute intersection numbers on the moduli space of curves using geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP 1 model using a superpotential e X +e t0,Q e −X given by the Lax operator of the Toda hierarchy (X is the LG field and t 0,Q is the coupling constant of the Kähler class). The form of the superpotential indicates the close connection between CP 1 and N = 2 supersymmetric sine-Gordon theory which was noted some time ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present a LG formulation of the topological CP 2 model.

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CALCULATION OF GROMOV-WITTEN INVARIANTS FOR CP³, CP⁴AND Gr(2, 4)

Cited by 8 publications

References 9 publications

Quantum cohomology and Virasoro algebra

Quantum cohomology and Virasoro algebra

Disk amplitudes in the topological A-model on Calabi-Yau spaces and Fano manifolds

Topological σ-models and the large-N matrix integrals

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