A super-current with independently assigned bosonic and fermionic monodromies generates super-Miwa differential constraints in all four sectors, linked by an explicit prefactor whose Grassmann kernel is the difference of the two fermion two-point functions.
Zvonkine,Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture, 2004
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Quantum Airy Structures and Matrix Models: a supercurrent approach
A super-current with independently assigned bosonic and fermionic monodromies generates super-Miwa differential constraints in all four sectors, linked by an explicit prefactor whose Grassmann kernel is the difference of the two fermion two-point functions.