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Volumn 5, Issue 4, 1999, Pages 423-466

Frobenius manifolds and Virasoro constraints

Author keywords

Frobenius manifold; Symmetry; Virasoro constraint

Indexed keywords


EID: 0000485488     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050053     Document Type: Article
Times cited : (82)

References (42)
  • 1
  • 3
    • 0011396411 scopus 로고
    • On classification of N = 2 supersymmetric theories
    • S. Cecotti and C. Vafa. On classification of N = 2 supersymmetric theories. Commun. Math. Phys. 158 (1993), 569-644.
    • (1993) Commun. Math. Phys. , vol.158 , pp. 569-644
    • Cecotti, S.1    Vafa, C.2
  • 6
    • 0000818276 scopus 로고
    • Mean field theory, topological field theory, and multi-matrix models
    • R. Dijkgraaf and E. Witten. Mean field theory, topological field theory, and multi-matrix models. Nucl. Phys. B342 (1990), 486-522.
    • (1990) Nucl. Phys. , vol.B342 , pp. 486-522
    • Dijkgraaf, R.1    Witten, E.2
  • 7
    • 0000817931 scopus 로고
    • Loop equations and Virasoro constraints in non-perturbative two-dimensional quantum gravity
    • R. Dijkgraaf, E. Verlinde and H.Verlinde. Loop equations and Virasoro constraints in non-perturbative two-dimensional quantum gravity. Nucl. Phys. 348 (1991), 435-456.
    • (1991) Nucl. Phys. , vol.348 , pp. 435-456
    • Dijkgraaf, R.1    Verlinde, E.2    Verlinde, H.3
  • 9
    • 0347427534 scopus 로고
    • Integrable systems in topological field theory
    • B. Dubrovin. Integrable systems in topological field theory. Nucl. Phys. B379 (1992), 627-689.
    • (1992) Nucl. Phys. , vol.B379 , pp. 627-689
    • Dubrovin, B.1
  • 10
    • 0039035170 scopus 로고
    • Topological conformai field theory from the point of view of integrable systems
    • L. Bonora, G. Mussardo, A. Schwimmer, L. Girardello, and M. Martellini, eds.
    • B. Dubrovin. Topological conformai field theory from the point of view of integrable systems,. In: Integrable Quantum Field Theories (L. Bonora, G. Mussardo, A. Schwimmer, L. Girardello, and M. Martellini, eds.), vol. B310. Plenum Press, NATO ASI series, 1993, pp. 283-302.
    • (1993) Integrable Quantum Field Theories , vol.B310 , pp. 283-302
    • Dubrovin, B.1
  • 12
    • 0000644797 scopus 로고    scopus 로고
    • Geometry of 2D topological field theories
    • M. Francaviglia, S. Greco, eds., Springer Lecture Notes in Math.
    • B. Dubrovin. Geometry of 2D topological field theories. In: Integrable Systems and Quantum Groups, Montecatini, Terme, 1993 (M. Francaviglia, S. Greco, eds.), vol. 1620. Springer Lecture Notes in Math., 1996, pp. 120-348.
    • (1996) Integrable Systems and Quantum Groups, Montecatini, Terme, 1993 , vol.1620 , pp. 120-348
    • Dubrovin, B.1
  • 13
    • 0000644797 scopus 로고    scopus 로고
    • Painlevé equations in 2D topological field theories
    • Cargèse, math.ag/9803107.
    • B. Dubrovin. Painlevé equations in 2D topological field theories. In: Painlevé Property, One Century Later. Cargèse, 1996, math.ag/9803107.
    • (1996) Painlevé Property, One Century Later.
    • Dubrovin, B.1
  • 14
    • 0041341381 scopus 로고    scopus 로고
    • Geometry and analytic theory of Frobenius manifolds
    • B. Dubrovin. Geometry and analytic theory of Frobenius manifolds. Proceedings of ICM98, Vol. II, 315-326.
    • Proceedings of ICM98 , vol.2 , pp. 315-326
    • Dubrovin, B.1
  • 16
    • 0001392731 scopus 로고
    • The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogoliubov-Whitham averaging method
    • B. Dubrovin and S.P. Novikov. The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogoliubov-Whitham averaging method. Sov. Math. Dokl. 27 (1983), 665-669.
    • (1983) Sov. Math. Dokl. , vol.27 , pp. 665-669
    • Dubrovin, B.1    Novikov, S.P.2
  • 17
    • 0000322926 scopus 로고    scopus 로고
    • Extended affine Weyl groups and Frobenius manifolds
    • B. Dubrovin and Y. Zhang. Extended affine Weyl groups and Frobenius manifolds. Compositio Math. 111 (1998), 167-219.
    • (1998) Compositio Math. , vol.111 , pp. 167-219
    • Dubrovin, B.1    Zhang, Y.2
  • 18
    • 0032276702 scopus 로고    scopus 로고
    • Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation
    • B. Dubrovin and Y. Zhang. Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Commun. Math. Phys. 198 (1998), 311-361.
    • (1998) Commun. Math. Phys. , vol.198 , pp. 311-361
    • Dubrovin, B.1    Zhang, Y.2
  • 19
    • 0041760335 scopus 로고    scopus 로고
    • Quantum Cohomology and Virasoro Algebra
    • T. Eguchi, K. Hori and C.-S. Xiong. Quantum Cohomology and Virasoro Algebra. Phys. Lett. B402 (1997), 71-80.
    • (1997) Phys. Lett. , vol.B402 , pp. 71-80
    • Eguchi, T.1    Hori, K.2    Xiong, C.-S.3
  • 20
    • 0032567580 scopus 로고    scopus 로고
    • Quantum Cohomology and Free Field Representation
    • T. Eguchi, M. Jinzenji and C.-S. Xiong. Quantum Cohomology and Free Field Representation. Nucl. Phys. B 510 (1998), 608-622.
    • (1998) Nucl. Phys. B , vol.510 , pp. 608-622
    • Eguchi, T.1    Jinzenji, M.2    Xiong, C.-S.3
  • 21
    • 0000913607 scopus 로고
    • Continuum Schwinger-Dyson equations and universal structures in two-dimensional gravity
    • M. Fukuma, H. Kawai and R. Nakayama. Continuum Schwinger-Dyson equations and universal structures in two-dimensional gravity. Int. J. Mod. Phys. A 6 (1991), 1385-1406.
    • (1991) Int. J. Mod. Phys. A , vol.6 , pp. 1385-1406
    • Fukuma, M.1    Kawai, H.2    Nakayama, R.3
  • 22
    • 0031533432 scopus 로고    scopus 로고
    • 1,4 and elliptic Gromov-Witten invariants, alg-geom/ 9612004
    • 1,4 and elliptic Gromov-Witten invariants, alg-geom/ 9612004. J. Amer. Math. Soc. 10 (1997), 973-998.
    • (1997) J. Amer. Math. Soc. , vol.10 , pp. 973-998
    • Getzler, E.1
  • 25
    • 0038058151 scopus 로고    scopus 로고
    • Elliptic Gromov-Witten invariants and generalized mirror conjecture
    • M.-H. Saito, Y. Shimizu and K. Veno, eds.. World Scientific
    • A.B. Givental. Elliptic Gromov-Witten invariants and generalized mirror conjecture. In: Integrable systems and algebraic geometry, Proceedings of the Taniguchi Symposium 1997 (M.-H. Saito, Y. Shimizu and K. Veno, eds.). World Scientific, 1998, pp. 107-155.
    • (1998) Integrable Systems and Algebraic Geometry, Proceedings of the Taniguchi Symposium 1997 , pp. 107-155
    • Givental, A.B.1
  • 26
    • 0003566247 scopus 로고
    • On the symmetries of integrable systems
    • A.S. Fokas and V.E. Zakharov, eds.. Springer-Verlag
    • P.G. Grinevich, A.Yu. Orlov and E.I. Schulman. On the symmetries of integrable systems. In: Important Developments in Soliton Theory (A.S. Fokas and V.E. Zakharov, eds.). Springer-Verlag, 1993, pp. 283-301.
    • (1993) Important Developments in Soliton Theory , pp. 283-301
    • Grinevich, P.G.1    Orlov, A.Y.2    Schulman, E.I.3
  • 28
    • 0000809447 scopus 로고
    • Constraints for topological strings in d ≥ 1
    • K. Hori. Constraints for topological strings in d ≥ 1. Nucl. Phys. B439 (1995), 395.
    • (1995) Nucl. Phys. , vol.B439 , pp. 395
    • Hori, K.1
  • 29
    • 49049148970 scopus 로고
    • Monodromy preserving deformations of linear ordinary differential equations with rational coefficients II
    • M. Jimbo and T. Miwa. Monodromy preserving deformations of linear ordinary differential equations with rational coefficients II. Physica D l (1981), 407-448.
    • (1981) Physica D , vol.50 , pp. 407-448
    • Jimbo, M.1    Miwa, T.2
  • 31
    • 0001792752 scopus 로고
    • Intersection theory on the moduli space of curves and the matrix Airy function
    • M. Kontsevich. Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys. 147 (1992), 1-23.
    • (1992) Comm. Math. Phys. , vol.147 , pp. 1-23
    • Kontsevich, M.1
  • 32
    • 34249763252 scopus 로고
    • Gromov-Witten classes, quantum cohomology, and enumerative geometry
    • M. Kontsevich and Yu. Manin. Gromov-Witten classes, quantum cohomology, and enumerative geometry. Comm. Math. Phys. 164 (1994), 525-562.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 525-562
    • Kontsevich, M.1    Manin, Yu.2
  • 33
    • 0000266512 scopus 로고
    • Topological gravity with minimal matter
    • Recursion relation in topological gravity with minimal matter, ibid 725.
    • K. Li. Topological gravity with minimal matter. Nucl. Phys. B 354 (1991), 711; Recursion relation in topological gravity with minimal matter, ibid 725.
    • (1991) Nucl. Phys. B , vol.354 , pp. 711
    • Li, K.1
  • 35
    • 36749117832 scopus 로고
    • A simple model of the integrable Hamiltonian systems
    • F. Magri. A simple model of the integrable Hamiltonian systems. J. Math. Phys. 19 (1978), 1156-1162.
    • (1978) J. Math. Phys. , vol.19 , pp. 1156-1162
    • Magri, F.1
  • 38
    • 0029682448 scopus 로고
    • A mathematical theory of quantum cohomology
    • Y. Ruan and G. Tian. A mathematical theory of quantum cohomology. J. Diff. Geom. 42 (1995), 259-367.
    • (1995) J. Diff. Geom. , vol.42 , pp. 259-367
    • Ruan, Y.1    Tian, G.2
  • 40
    • 0009243741 scopus 로고
    • On the structure of the topological phase of two-dimensional gravity
    • E. Witten. On the structure of the topological phase of two-dimensional gravity. Nucl. Phys. B340 (1990), 281-332.
    • (1990) Nucl. Phys. , vol.B340 , pp. 281-332
    • Witten, E.1
  • 41
    • 0000910190 scopus 로고
    • Two-dimensional gravity and intersection theory on moduli space
    • E. Witten. Two-dimensional gravity and intersection theory on moduli space. Surv. in Diff. Geom. 1 (1991), 243-310.
    • (1991) Surv. in Diff. Geom. , vol.1 , pp. 243-310
    • Witten, E.1


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