WDVV Equations as Functional Relations
نویسندگان
چکیده
The associativity or Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations [1] have been widely discussed in connection with various problems of mathematical physics for over ten years. They have arisen in the context of quantum cohomologies and mirror symmetry, and also with regard to multidimensional supersymmetric gauge field theories. In their most general form these equations may be expressed as [2]
منابع مشابه
Associativity Relations in Quantum Cohomology
We describe interdependencies among the quantum cohomology associativity relations. We strengthen the first reconstruction theorem of Kontsevich and Manin by identifying a subcollection of the associativity relations which implies the full system of WDVV equations. This provides a tool for identifying non-geometric solutions to WDVV.
متن کاملWeyl Groups and Elliptic Solutions of the Wdvv Equations
A functional ansatz is developed which gives certain elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equation. This is based on the elliptic trilogarithm function introduced by Beilinson and Levin. For this to be a solution results in a number of purely algebraic conditions on the set of vectors that appear in the ansatz, this providing an elliptic version of the idea, in...
متن کاملar X iv : h ep - t h / 02 01 26 7 v 1 3 1 Ja n 20 02 FIAN / TD - 02 / 02 ITEP / TH - 04 / 02 On Associativity Equations 1
We consider the associativity or Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations and discuss one of the most relevant for non-perturbative physics class of their solutions based on existence of the residue formulas. It is demonstrated for this case that the proof of associativity equations is reduced to the problem of solving system of algebraic linear equations. The particular examples of ...
متن کاملOn Associativity Equations 1
We consider the associativity or Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations and discuss one of the most relevant for non-perturbative physics class of their solutions based on existence of the residue formulas. It is demonstrated for this case that the proof of associativity equations is reduced to the problem of solving system of algebraic linear equations. The particular examples of ...
متن کاملOn Integrable Structure behind the Generalized WDVV Equations
In the theory of quantum cohomologies the WDVV equations imply integrability of the system (I∂μ− zCμ)ψ = 0. However, in generic situation – of which an example is provided by the Seiberg-Witten theory – there is no distinguished direction (like t) in the moduli space, and such equations for ψ appear inconsistent. Instead they are substituted by (Cμ∂ν−Cν∂μ)ψ ∼ (Fμ∂ν−Fν∂μ)ψ = 0, where matrices (F...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002