We find the transformation properties of the prepotential F of N = 2 SUSY gauge theory with gauge group SU(2). Next we show that G(a) = πi(F(a) -1/2a ∂aF(a)) is modular invariant. We also show that u = G(a), so that F(<φ>) =1/πi <tr φ2> + 1/2<φ><φD>. This implies thatG (a) satisfies the non-linear differential equation (1 - G2) G'' +1/4aG '3 = 0. We use this equation to derive recursion relations for the instanton contributions. These results can be extended to more general cases.

INSTANTONS AND RECURSION RELATIONS IN N=2 SUSY GAUGE THEORY

MATONE, MARCO
1995

Abstract

We find the transformation properties of the prepotential F of N = 2 SUSY gauge theory with gauge group SU(2). Next we show that G(a) = πi(F(a) -1/2a ∂aF(a)) is modular invariant. We also show that u = G(a), so that F(<φ>) =1/πi + 1/2<φ><φD>. This implies thatG (a) satisfies the non-linear differential equation (1 - G2) G'' +1/4aG '3 = 0. We use this equation to derive recursion relations for the instanton contributions. These results can be extended to more general cases.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/120415
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