This article is cited in 1 paper

Whitham hierarchy and generalized Picard–Fuchs operators in the $\mathcal N=2$ SUSY Yang–Mills theory for classical gauge groups

Jialiang Dai^a, Engui Fan<sup>b

a</sup> Department of Physics, Zhejiang University, Shanghai, China
^b School of Mathematical Science, Fudan University, Shanghai, China

Abstract: We derive infinitely many meromorphic differentials based on the fractional powers of the superpotential arising from hyperelliptic curves. We obtain various differential equations expressed in terms of the moduli derivatives of the Seiberg–Witten differential. Taking advantage of the cross derivatives of these differentials, we can derive some Picard–Fuchs equations and use the Euler operator to obtain a complete set of Picard–Fuchs equations containing the instanton correction term. We solve the complete system of equations by expanding the moduli parameters in power series.

Keywords: Whitham hierarchy, Picard–Fuchs equation, instanton correction, renormalization group parameter.

Received: 04.05.2018
Revised: 04.05.2018

DOI: 10.4213/tmf9587

 English version: Theoretical and Mathematical Physics, 2019, 198:3, 317–330

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