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TMF, 2002, Volume 132, Number 1, Pages 3–49 (Mi tmf344)  

This article is cited in 13 scientific papers (total in 13 papers)

On Associativity Equations

A. V. Marshakov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We consider the associativity or Witten–Dijkgraaf–Verlinde–rlinde (WDVV) equations and discuss their solution class based on the existence of the residue formulas, which is most relevant for nonperturbative physics. We demonstrate that for this case, proving the associativity equations reduces to solving a stem of linear algebraic equations. Particular examples of solutions related to Landau–Ginzburg topological theories, Seiberg–Witten theories, and the tau functions of semiclassical hierarchies are discussed in detail. We also discuss related questions including the covariance of associativity equations, their relation to dispersionless Hirota relations, and the auxiliary linear problem for the WDVV equations.

Keywords: associativity equations, Seiberg–Witten theory, integrable systems, topological theories, special Kähler geometry


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English version:
Theoretical and Mathematical Physics, 2002, 132:1, 895–933

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Received: 09.01.2002

Citation: A. V. Marshakov, “On Associativity Equations”, TMF, 132:1 (2002), 3–49; Theoret. and Math. Phys., 132:1 (2002), 895–933

Citation in format AMSBIB
\by A.~V.~Marshakov
\paper On Associativity Equations
\jour TMF
\yr 2002
\vol 132
\issue 1
\pages 3--49
\jour Theoret. and Math. Phys.
\yr 2002
\vol 132
\issue 1
\pages 895--933

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    This publication is cited in the following articles:
    1. Itoyama, H, “The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory”, Nuclear Physics B, 657:1–3 (2003), 53  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Itoyama, H, “Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case”, Physics Letters B, 555:3–4 (2003), 287  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Mironov, A, “N=1 SUSY inspired whitham prepotentials and WDVV”, Fortschritte der Physik-Progress of Physics, 51:7–8 (2003), 781  crossref  mathscinet  zmath  isi
    4. Chekhov, L, “DV and WDVV”, Physics Letters B, 562:3–4 (2003), 323  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Kazakov, VA, “Complex curve of the two-matrix model and its tau-function”, Journal of Physics A-Mathematical and General, 36:12 (2003), 3107  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Alexandrov A, Morozov A, Mironov A, “Partition functions of matrix models: First special functions of string theory”, International Journal of Modern Physics A, 19:24 (2004), 4127–4163  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. L. O. Chekhov, A. V. Marshakov, A. D. Mironov, D. Vasiliev, “Complex Geometry of Matrix Models”, Proc. Steklov Inst. Math., 251 (2005), 254–292  mathnet  mathscinet  zmath
    8. A. S. Alexandrov, A. D. Mironov, A. Yu. Morozov, “Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model”, Theoret. and Math. Phys., 142:3 (2005), 349–411  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. A. V. Marshakov, “Matrix models, complex geometry, and integrable systems: II$^*$”, Theoret. and Math. Phys., 147:3 (2006), 777–820  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Chekhov, L, “Matrix models with hard walls: geometry and solutions”, Journal of Physics A-Mathematical and General, 39:28 (2006), 8857  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. Braden, HW, “WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves”, Acta Applicandae Mathematicae, 99:3 (2007), 223  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Konishi, E, “Planar homological mirror symmetry”, International Journal of Modern Physics A, 22:29 (2007), 5351  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Gavrylenko P., Marshakov A., “Residue Formulas For Prepotentials, Instanton Expansions and Conformal Blocks”, J. High Energy Phys., 2014, no. 5, 097  crossref  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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