×

zbMATH — the first resource for mathematics

Chern-Simons theory and topological strings. (English) Zbl 1205.81013
Summary: A review of the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces is given. This relation has made it possible to give an exact solution of topological string theory on these spaces to all orders in the string coupling constant. Here the focus is on the construction of this solution, which is encoded in the topological vertex, and the implications of the physics of string/gauge theory duality for knot theory and for the geometry of Calabi-Yau manifolds.

MSC:
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T45 Topological field theories in quantum mechanics
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Aganagic, M., J. High Energy Phys. 0402 pp 010– (2004) ISSN: http://id.crossref.org/issn/1126-6708 · doi:10.1088/1126-6708/2004/02/010
[2] Aganagic, M., Z. Naturforsch., A: Phys. Sci. 57 pp 1– (2002) ISSN: http://id.crossref.org/issn/0932-0784 · doi:10.1515/zna-2002-9-1001
[3] DOI: 10.1007/s00220-004-1067-x · Zbl 1055.81055 · doi:10.1007/s00220-004-1067-x
[4] DOI: 10.1016/0550-3213(94)90617-3 · Zbl 1007.81522 · doi:10.1016/0550-3213(94)90617-3
[5] DOI: 10.1016/0040-9383(90)90021-B · Zbl 0716.57011 · doi:10.1016/0040-9383(90)90021-B
[6] DOI: 10.1063/1.1376159 · Zbl 1061.81056 · doi:10.1063/1.1376159
[7] DOI: 10.1016/0550-3213(95)00487-1 · Zbl 0925.81161 · doi:10.1016/0550-3213(95)00487-1
[8] DOI: 10.1016/0550-3213(93)90548-4 · Zbl 0908.58074 · doi:10.1016/0550-3213(93)90548-4
[9] DOI: 10.1007/BF02099774 · Zbl 0815.53082 · doi:10.1007/BF02099774
[10] DOI: 10.1016/0370-2693(90)91899-M · doi:10.1016/0370-2693(90)91899-M
[11] DOI: 10.1016/0550-3213(90)90577-Z · doi:10.1016/0550-3213(90)90577-Z
[12] Chiang, T. M., Adv. Theor. Math. Phys. 3 pp 495– (1999) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 0976.32012 · doi:10.4310/ATMP.1999.v3.n3.a3
[13] Coleman, S., in: Aspects of Symmetry (1988)
[14] DOI: 10.1016/0370-2693(94)91447-8 · doi:10.1016/0370-2693(94)91447-8
[15] Cox, D., in: Mirror Symmetry and Algebraic Geometry (1999) · Zbl 0951.14026
[16] Diaconescu, D. E., Adv. Theor. Math. Phys. 6 pp 619– (2003) ISSN: http://id.crossref.org/issn/1095-0761 · doi:10.4310/ATMP.2002.v6.n4.a2
[17] Diaconescu, D. E., Adv. Theor. Math. Phys. 6 pp 643– (2003) ISSN: http://id.crossref.org/issn/1095-0761 · doi:10.4310/ATMP.2002.v6.n4.a3
[18] Di Francesco, P., in: Conformal Field Theory (1997) · doi:10.1007/978-1-4612-2256-9
[19] Dijkgraaf, R., in: String Theory and Quantum Gravity (1991)
[20] Eguchi, T., J. High Energy Phys. 0312 pp 006– (2003) ISSN: http://id.crossref.org/issn/1126-6708 · doi:10.1088/1126-6708/2003/12/006
[21] DOI: 10.1016/j.physletb.2004.01.085 · Zbl 1246.81120 · doi:10.1016/j.physletb.2004.01.085
[22] DOI: 10.1016/0550-3213(89)90436-7 · doi:10.1016/0550-3213(89)90436-7
[23] Faber, C., in: New Trends in Algebraic Geometry (1999)
[24] Faber, C., Invent. Math. 139 pp 173– (2000) ISSN: http://id.crossref.org/issn/0020-9910 · Zbl 0960.14031 · doi:10.1007/s002229900028
[25] DOI: 10.1007/BF02100006 · Zbl 0739.53065 · doi:10.1007/BF02100006
[26] DOI: 10.1090/S0273-0979-1985-15361-3 · Zbl 0572.57002 · doi:10.1090/S0273-0979-1985-15361-3
[27] Fulton, W., in: Representation Theory. A First Course (1991)
[28] DOI: 10.1016/S0550-3213(98)00517-3 · Zbl 0957.14038 · doi:10.1016/S0550-3213(98)00517-3
[29] Gopakumar, R., Adv. Theor. Math. Phys. 3 pp 1415– (1999) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 0972.81135 · doi:10.4310/ATMP.1999.v3.n5.a5
[30] Graber, T., Contemp. Math. 310 pp 107– (2002) ISSN: http://id.crossref.org/issn/0271-4132 · doi:10.1090/conm/310/05400
[31] DOI: 10.1016/0550-3213(93)90402-B · Zbl 0941.81580 · doi:10.1016/0550-3213(93)90402-B
[32] DOI: 10.1016/0550-3213(93)90403-C · Zbl 0941.81586 · doi:10.1016/0550-3213(93)90403-C
[33] DOI: 10.1142/S0217751X92000417 · Zbl 0821.57004 · doi:10.1142/S0217751X92000417
[34] DOI: 10.1016/0550-3213(90)90124-V · doi:10.1016/0550-3213(90)90124-V
[35] Harris, J., in: Moduli of Curves (1998)
[36] DOI: 10.1007/BF02392726 · Zbl 0584.53021 · doi:10.1007/BF02392726
[37] Hori, K., in: Mirror Symmetry (2003) · Zbl 1069.81562
[38] Iqbal, A., Adv. Theor. Math. Phys. 7 pp 457– (2003) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 1044.32022 · doi:10.4310/ATMP.2003.v7.n3.a4
[39] DOI: 10.1007/BF02097243 · Zbl 0755.53054 · doi:10.1007/BF02097243
[40] DOI: 10.1063/1.1590055 · Zbl 1062.37071 · doi:10.1063/1.1590055
[41] DOI: 10.1016/S0550-3213(97)00282-4 · Zbl 0935.81058 · doi:10.1016/S0550-3213(97)00282-4
[42] Katz, S., Adv. Theor. Math. Phys. 3 pp 1445– (1999) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 0985.81081 · doi:10.4310/ATMP.1999.v3.n5.a6
[43] Katz, S., Adv. Theor. Math. Phys. 5 pp 1– (2002) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 1026.32028 · doi:10.4310/ATMP.2001.v5.n1.a1
[44] Klemm, A., in: Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (2001)
[45] DOI: 10.1007/BF02099526 · Zbl 0756.35081 · doi:10.1007/BF02099526
[46] Kontsevich, M., Prog. Math. 129 pp 335– (1995) ISSN: http://id.crossref.org/issn/0743-1643
[47] Labastida, J. M. F., in: Trends in Theoretical Physics II (1999)
[48] DOI: 10.1016/0550-3213(92)90596-4 · doi:10.1016/0550-3213(92)90596-4
[49] DOI: 10.1007/s002200100374 · Zbl 1018.81049 · doi:10.1007/s002200100374
[50] DOI: 10.1142/S0218216502001561 · Zbl 1002.57026 · doi:10.1142/S0218216502001561
[51] Labastida, J. M. F., J. High Energy Phys. 0011 pp 007– (2000) ISSN: http://id.crossref.org/issn/1126-6708 · Zbl 0990.81545 · doi:10.1088/1126-6708/2000/11/007
[52] DOI: 10.1016/0370-2693(89)91289-6 · doi:10.1016/0370-2693(89)91289-6
[53] Leung, N. C., Adv. Theor. Math. Phys. 2 pp 91– (1998) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 0914.14024 · doi:10.4310/ATMP.1998.v2.n1.a4
[54] Li, J., Adv. Theor. Math. Phys. 5 pp 67– (2002) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 1015.14026 · doi:10.4310/ATMP.2001.v5.n1.a3
[55] Lickorish, W. B. R., in: An Introduction to Knot Theory (1998)
[56] Liu, C.-C. M., J. Diff. Geom. 65 pp 289– (2003) ISSN: http://id.crossref.org/issn/0022-040X
[57] Macdonald, I. G., in: Symmetric Functions and Hall Polynomials (1995) · Zbl 0824.05059
[58] Maldacena, J. M., Adv. Theor. Math. Phys. 2 pp 231– (1998) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 0914.53047 · doi:10.4310/ATMP.1998.v2.n2.a1
[59] DOI: 10.1016/S0550-3213(98)00847-5 · Zbl 0951.14037 · doi:10.1016/S0550-3213(98)00847-5
[60] Mariño, M., Contemp. Math. 310 pp 185– (2002) ISSN: http://id.crossref.org/issn/0271-4132 · doi:10.1090/conm/310/05404
[61] DOI: 10.1142/S0218216503002536 · Zbl 1055.57014 · doi:10.1142/S0218216503002536
[62] DOI: 10.2140/gt.2004.8.675 · Zbl 1062.14035 · doi:10.2140/gt.2004.8.675
[63] DOI: 10.1016/0550-3213(96)00379-3 · Zbl 0925.14008 · doi:10.1016/0550-3213(96)00379-3
[64] DOI: 10.1016/S0550-3213(00)00118-8 · Zbl 1036.81515 · doi:10.1016/S0550-3213(00)00118-8
[65] DOI: 10.1016/S0550-3213(02)00620-X · Zbl 0998.81073 · doi:10.1016/S0550-3213(02)00620-X
[66] DOI: 10.1103/PhysRevLett.71.1295 · Zbl 0972.81596 · doi:10.1103/PhysRevLett.71.1295
[67] Polchinski, J., in: String Theory (1998) · doi:10.1017/CBO9780511618123
[68] DOI: 10.1142/S0217732388000398 · doi:10.1142/S0217732388000398
[69] Prasolov, V. V., in: Knots, Links, Braids and 3-manifolds (1997)
[70] DOI: 10.1016/S0550-3213(00)00761-6 · Zbl 1097.81742 · doi:10.1016/S0550-3213(00)00761-6
[71] DOI: 10.1007/BF02099272 · Zbl 0837.57014 · doi:10.1007/BF02099272
[72] DOI: 10.1016/0550-3213(94)90124-4 · Zbl 0996.81510 · doi:10.1016/0550-3213(94)90124-4
[73] DOI: 10.1016/0550-3213(94)00449-8 · Zbl 0996.81511 · doi:10.1016/0550-3213(94)00449-8
[74] Taubes, C. H., Adv. Theor. Math. Phys. 5 pp 139– (2001) ISSN: http://id.crossref.org/issn/1095-0761 · Zbl 1022.53057 · doi:10.4310/ATMP.2001.v5.n1.a5
[75] DOI: 10.1016/S0550-3213(00)00338-2 · Zbl 0984.81126 · doi:10.1016/S0550-3213(00)00338-2
[76] DOI: 10.1016/0550-3213(74)90154-0 · doi:10.1016/0550-3213(74)90154-0
[77] Vafa, C., J. Math. Phys. 42 pp 2798– (2001) ISSN: http://id.crossref.org/issn/0022-2488 · Zbl 1060.81594 · doi:10.1063/1.1376161
[78] DOI: 10.1016/0550-3213(86)90155-0 · doi:10.1016/0550-3213(86)90155-0
[79] DOI: 10.1007/BF01466725 · Zbl 0674.58047 · doi:10.1007/BF01466725
[80] DOI: 10.1007/BF01217730 · Zbl 0667.57005 · doi:10.1007/BF01217730
[81] DOI: 10.1016/0550-3213(90)90449-N · doi:10.1016/0550-3213(90)90449-N
[82] Witten, E., Surv. Diff. Geom. 1 pp 243– (1991) · doi:10.4310/SDG.1990.v1.n1.a5
[83] DOI: 10.1016/0550-3213(93)90033-L · Zbl 0910.14020 · doi:10.1016/0550-3213(93)90033-L
[84] Witten, E., Prog. Math. 133 pp 637– (1995) ISSN: http://id.crossref.org/issn/0743-1643
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.