Abstract
Using the Whitham hierarchy, we obtain the Picard—Fuchs equations in\({\mathcal N} = 2\)supersymmetric Yang—Mills theory for a classical gauge group with Nfmassless hypermultiplets. In the general case for Nf ≠ 0, there are at least r−2 Picard—Fuchs equations that can be computed exactly from the commutation relations of the meromorphic differentials defined up to a linear combination of holomorphic differentials on the Seiberg—Witten hyperelliptic curve. Using Euler operator techniques, we study the Picard—Fuchs equations, including instanton corrections. Moreover, using symbolic computer calculations, we can obtain a complete set of Picard—Fuchs equations.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 2, pp. 170–186, February, 2020.
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Dai, J. Generalized Picard—Fuchs Operators From Whitham Hierarchy in \({\mathcal N} = 2\) Supersymmetric Gauge Theory with Massless Hypermultiplets. Theor Math Phys 202, 150–164 (2020). https://doi.org/10.1134/S0040577920020026
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DOI: https://doi.org/10.1134/S0040577920020026