Theoretical and Mathematical Physics

, Volume 198, Issue 3, pp 317–330 | Cite as

Whitham Hierarchy and Generalized Picard–Fuchs Operators in the N=2 Susy Yang–Mills Theory for Classical Gauge Groups

  • Jialiang DaiEmail author
  • Engui Fan


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.


Whitham hierarchy Picard–Fuchs equation instanton correction renormalization group parameter 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of PhysicsZhejiang UniversityHangzhouChina
  2. 2.School of Mathematical ScienceFudan UniversityShanghaiChina

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