Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-09-25
J.Math.Phys. 40 (1999) 1891-1900
Physics
High Energy Physics
High Energy Physics - Theory
revtex
Scientific paper
Differential equations for scaling relation of prepotential in N=2 supersymmetric SU(2) Yang-Mills theory coupled with massive matter hypermultiplet are proposed and are explicitly demonstrated in one flavour ($N_f =1$) theory. By applying Whitham dynamics, the first order derivative of the prepotential over the $T_0$ variable corresponding to the mass of the hypermultiplet, which has a line integral representation, is found to satisfy a differential equation. As the result, the closed form of this derivative can be obtained by solving this equation. In this way, the scaling relation of massive prepotential is established. Furthermore, as an application of another differential equation for the massive scaling relation, the massive prepotential in strong coupling region is derived.
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