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arXiv · hep-th/9510183

Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations

Tohru Eguchi·Sung-Kil Yang
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Abstract

Using recently proposed soliton equations we derive a basic identity for the scaling violation of $N=2$ supersymmetric gauge theories $\sum_i a_i\partial F/\partial a_i-2F=8 πi b_1 u$. Here $F$ is the prepotential, $a_i$'s are the expectation values of the scalar fields in the vector multiplet, $u=1/2\, {\rm Tr}\, \langleϕ^2\rangle$ and $b_1$ is the coefficient of the one-loop $β$-function. This equation holds in the Coulomb branch of all $N=2$ supersymmetric gauge theories coupled with massless matter.

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Tohru Eguchi, Sung-Kil Yang. 1995-10-27. Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations. https://doi.org/10.1142/s0217732396000151

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