On Associativity Equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 3-49

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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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     author = {A. V. Marshakov},
     title = {On {Associativity} {Equations}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a0/}
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A. V. Marshakov. On Associativity Equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 132 (2002) no. 1, pp. 3-49. http://geodesic.mathdoc.fr/item/TMF_2002_132_1_a0/