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.
Duality and integrability of supermatrix model with external source
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abstract
We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the one and two dimensional Toda lattice equations as well as the ordinary matrix model.
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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.