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String theory and classical integrable systems

  • A. Marshakov
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 436)

Abstract

We discuss different formulations and approaches to string theory and 2d quantum gravity. The generic idea to get a unique description of many different string vacua altogether is demonstrated on the examples in 2d conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of generalizations to “higher-dimensional” models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.

Keywords

String Theory Matrix Model Topological String Module Space Topological Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M.Douglas Phys.Lett., 238B (1990) 176Google Scholar
  2. [2]
    M.Fukuma, H.Kawai, and R.Nakayama Int.J.Mod.Phys., A6 (1991) 1385Google Scholar
  3. [3]
    R.Dijkgraaf, H.Verlinde, and E.Verlinde, Nucl.Phys., B348 (1991) 435.Google Scholar
  4. [4]
    A.Gerasimov et al. Nucl.Phys., B357 (1991) 565.Google Scholar
  5. [5]
    S.Kharchev et al. Nucl.Phys., B380 (1992) 181Google Scholar
  6. [6]
    E.Witten, Chern-Simons theory as a string theory, Preprint IASSNS-HEP-92-45.Google Scholar
  7. [7]
    B.Zwiebach Nucl.Phys. B390 (1993) 33.Google Scholar
  8. [8]
    A.Marshakov, On string field theory for c ≤ 1, preprint FIAN/TD108-92 (June, 1992), hepth/9208022; in Pathways to Fundamental Theories, World Scientific, 1993.Google Scholar
  9. [9]
    E.Witten, Nucl.Phys. B340 (1990) 281; Surveys Diff.Geom. 1 (1991) 243 R.Dijkgraaf and E.Witten, Nucl.Phys B342 486Google Scholar
  10. [10]
    J. Distler, Nucl.Phys B342 (1990) 523Google Scholar
  11. [11]
    A.Gerasimov et al Phys.Lett. B242 (1990) 345.Google Scholar
  12. [12]
    M.Kontsevich, Comm. Math.Phys. 147 (1992) 1.Google Scholar
  13. [13]
    E.Witten On the Kontsevich model and other models of 2d gravity, Preprint IASSNS-HEP-91-24.Google Scholar
  14. [14]
    A.Marshakov, A.Mironov, and A.Morozov, Phys.Lett., B274 (1992) 280.Google Scholar
  15. [15]
    A.Mikhailov Int.J.Mod.Phys. A9 (1994) 873Google Scholar
  16. [16]
    R.Dijkgraaf, E. Verlinde and H. Verlinde, Nucl.Phys B352 (1991) 59Google Scholar
  17. [17]
    R.Dijkgraaf, Intersection theory, integrable hierarchies and topological field theory, preprint IASSNS-HEP-91/91Google Scholar
  18. [18]
    A.Lossev, Descendans constructed from matter fields and K.Saito higher residue pairing in Landau-Ginzburg theories coupled to topological gravity, preprint ITEP/TPI-MINN (May, 1992). A.Losev, I.Polyubin, On connection between topological Landau-Ginzburg gravity and integrable systems, preprint ITEP/Uppsala, (1993)Google Scholar
  19. [19]
    K.Li, Nucl.Phys. B354 (1991) 711Google Scholar
  20. [20]
    J.Duistermaat and G.Heckman, Invent.Math. 69 (1982) 259Google Scholar
  21. [20a]
    M.Atiyah, R.Bott, Topology 23, (1984) 1Google Scholar
  22. [20b]
    M.Blau, E.Keski-Vakkuri and A.Niemi, Phys.Lett. B246 (1990) 92Google Scholar
  23. [20c]
    E.Keski-Vakkuri, A.Niemi, G.Semenoff and O.Tirkkonen, Phys.Rev. D44 (1991) 3899Google Scholar
  24. [20c]
    A.Hietamaki, A.Morozov, A.Niemi, K.Palo Phys.Lett. 263B (1991) 417Google Scholar
  25. [20d]
    A.Morozov, A.Niemi, K.Palo Phys.Lett. 271B (1991) 365; Nucl.Phys. B377 (1992) 295Google Scholar
  26. [20e]
    A.Niemi and O.Tirkkonen, On Exact Evaluation of Path Integrals, Preprint UU-ITP, 3/93Google Scholar
  27. [21]
    M.Kontsevich A -algebras in mirror symmetry, Preprint (1994)Google Scholar
  28. [22]
    M.Kontsevich, Yu.Manin Gromov-Witten classes, quantum cohomology and enumerative geometry, Preprint (1994)Google Scholar
  29. [23]
    E.Witten Quantum background independence in string theory, preprint IASSNS-HEP-93/29Google Scholar
  30. [24]
    S.Kharchev, A.Marshakov Quantization of string theory for c>-1, Preprint FIAN/TD-14/93.Google Scholar
  31. [25]
    J.-L.Gervais Nucl.Phys. B391 (1993) 287Google Scholar
  32. [26]
    J.-L.Gervais, J.Schnittger Nucl.Phys. B413 (1994) 433 Phys.Lett. B315 (1993) 258.Google Scholar
  33. [27]
    V.Knizhnik, A.Polyakov, A.Zamolodchikov Mod.Phys.Lett. A3 (1988) 819Google Scholar
  34. [28]
    J.Distler, H.Kawal, Nucl.Phys. B312 (1989) 509Google Scholar
  35. [29]
    F.David, Mod.Phys.Lett. A3 (1988) 1651Google Scholar
  36. [30]
    Vl.Dotsenko Mod.Phys.Lett. A7 (1992) 2505.Google Scholar
  37. [31]
    M.Bershadsky, S.Cecotti, H.Ooguri and C.Vafa Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, preprint HUTP93/A025.Google Scholar
  38. [32]
    S.Kharchev et al. Landau-Ginzburg topological theories in the framework of GKM and equvalent hierarchies, preprint FIAN/TD/7-92, ITEP-M-5/92 (July, 1992), hepth/9208046.Google Scholar
  39. [33]
    S.Kharchev, A.Marshakov, Topological versus non-topological theories and p-q duality in matrix models, preprint FIANITD/15-92 (September, 1992), hepth/9210072; in String Theory, Quantum Gravity and the Unification of the Fundamental Interactions, World Scientific, 1993.Google Scholar
  40. [34]
    S.Kharchev, A.Marshakov, On p — q duality and explicit solutions in c >-1 2d gravity models, preprint NORDITA-93/20 P, FIAN/TD-04/93 Google Scholar
  41. [35]
    V.Kac, A.Schwarz, Phys.Lett. B257 (1991) 329Google Scholar
  42. [36]
    A.Schwarz, Mod.Phys.Lett. A6 (1991) 611; 2713Google Scholar
  43. [37]
    A.Gerasimov et al Phys.Lett. B236 (1990) 269Google Scholar
  44. [38]
    A.Gerasimov et al. Int.J.Mod.Phys., A5 (1990) 2495Google Scholar
  45. [39]
    G.Moore, N.Seiberg, M.Staudacher Nucl.Phys. B362 (1991) 665Google Scholar
  46. [40]
    C.Itzyzson and J.-B.Zuber, J.Math.Phys., 21 (1980) 411Google Scholar
  47. [40a]
    M.L.Mehta, Commun.Math.Phys., 79 (1981) 327Google Scholar
  48. [41]
    E.Date, M.Jimbo, M.Kashiwara, and T.Miwa, Transformation group for soliton equation: III, preprint RIMS-358 (1981)Google Scholar
  49. [41a]
    E.Date, M.Jimbo, M.Kashiwara, and T.Miwa. In: Proc.RIMS symp.Nonlinear integrable systems — classical theory and quantum theory, page 39, Kyoto, 1983.Google Scholar
  50. [42]
    G.Segal and G.Wilson, Publ.I.H.E.S., 61 (1985) 1.Google Scholar
  51. [43]
    I.Krichever, Comm.Math.Phys., 143 (1992) 415; The tau-function of the universal Whitham hierarchy, matrix models and topological field theories, preprint LPTENS-92/18. also talk at IV Conference on Mathematical Physics, Rakhov, 1994 and private communication.Google Scholar
  52. [44]
    V.Fock, A.Rosly Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix, preprint ITEP-72-92 Google Scholar
  53. [44a]
    V.Fock, A.Rosly Flat connections and polyubles, Theor. and Math. Phys., 95 (1993) 228.Google Scholar
  54. [45]
    D.Gross, W.Taylor, Twists and Wilson loops in the string theory of two dimensional QCD, Preprint CERN-TH.6827/93, PUPT-1382, LBL-33767, UCB-PTH-93/09Google Scholar
  55. [46]
    A.Gorsky, N.Nekrasov, Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory, Preprint UUITP-6/93, ITEP-20/93Google Scholar
  56. [47]
    C.Vafa, Mirror transform and string theory Google Scholar
  57. [48]
    S.Kharchev et al Generalized Kazakov-Migdal-Kontsevich model: group theory aspects, Preprint UUITP-10/93, FIAN/TD-07/93, ITEP-M4/93.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • A. Marshakov
    • 1
    • 2
  1. 1.Theory DepartmentP.N.Lebedev Physics InstituteMoscowRussia
  2. 2.Institute of Theoretical PhysicsUppsala UniversityUppsala

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