WDVV-like equations in N = 2 SUSY Yang-Mills theory

The prepotential F(ai); defining the low-energy effective action of the SU(N) N = 2 SUSY gluodynamics, satisfies an enlarged set of the WDVV-like equations FiFk−1Fj = FjFk−1Fi for any triple i, j, k = 1,…, N − 1, where matrix Fi is equal to (Fi)mn = ∂3F∂ai∂am∂an. The same equations are actually true for generic topological theories. In contrast to the conventional formulation, when k is restricted to k = 0, in the proposed system there is no distinguished “first” time-variable, and the indices can be raised with the help of any “metric” ηmn(k) = (Fk)mn, not obligatory flat. All the equations (for all i, j, k) are true simultaneously. This result provides a new parallel between the Seiberg-Witten theory of low-energy gauge models in 4d and topological theories.