On associativity equations

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13 Citations (Scopus)

Abstract

We consider the associativity or Witten-Dijkgraaf-Verlinde-Verlinde (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 system 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 WDW equations.

Original languageEnglish
Pages (from-to)895-933
Number of pages39
JournalTheoretical and Mathematical Physics
Volume132
Issue number1
DOIs
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • Associativity equations
  • Integrable systems
  • Seiberg-Witten theory
  • Special Kähler geometry
  • Topological theories

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