Geodesic
Generalized Picard--Fuchs operators from Whitham hierarchy in $\mathcal N=2$ supersymmetric gauge theory with massless hypermultiplets
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 170-186

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Using the Whitham hierarchy, we obtain the Picard–Fuchs equations in $\mathcal N=2$ supersymmetric Yang–Mills theory for a classical gauge group with $N_\mathrm{f}$ massless hypermultiplets. In the general case for $N_\mathrm{f}\ne0$, 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.
Mots-clés : Picard–Fuchs equation, instanton correction.
Keywords: Whitham hierarchy, meromorphic differential, Euler operator 
@article{TMF_2020_202_2_a1,
     author = {Jialiang Dai},
     title = {Generalized {Picard--Fuchs} operators from {Whitham} hierarchy in $\mathcal N=2$ supersymmetric gauge theory with massless hypermultiplets},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {170--186},
     publisher = {mathdoc},
     volume = {202},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a1/}
}
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Jialiang Dai. Generalized Picard--Fuchs operators from Whitham hierarchy in $\mathcal N=2$ supersymmetric gauge theory with massless hypermultiplets. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 170-186. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a1/