WDVV-like equations in [formula omitted] = 2 SUSY Yang-Mills theory

Abstract

The prepotential F( a i ); defining the low-energy effective action of the SU( N) N = 2 SUSY gluodynamics, satisfies an enlarged set of the WDVV-like equations F i F k −1 F j = F j F k −1 F i for any triple i, j, k = 1,…, N − 1, where matrix F i is equal to (F i) mn = ∂ 3F ∂a i∂a m∂a n . 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” η mn ( k) = ( F k ) 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 4 d and topological theories.