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Whitham hierarchy and generalized Picard-Fuchs operators in the \(\mathcal{N}=2\) susy Yang-Mills theory for classical gauge groups. (English. Russian original) Zbl 1419.81031

Theor. Math. Phys. 198, No. 3, 317-330 (2019); translation from Teor. Mat. Fiz. 198, No. 3, 365-380 (2019).
Summary: 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.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
14H52 Elliptic curves
81T17 Renormalization group methods applied to problems in quantum field theory
57R57 Applications of global analysis to structures on manifolds
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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