The gauge-origami folded instanton partition function yields the characteristic polynomial whose large-x expansion reproduces the commuting Hamiltonians of the elliptic double Calogero-Moser system.
N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
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The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous) $sl(2)$ spin chains with the length of the chain being equal to the number of colours $N_c$. For $N_f < 2N_c$ the relevant spin chain is the simplest $XXX$-model, and this identification is in agreement with the known results in Seiberg-Witten theory.
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Quantum Elliptic Calogero-Moser Systems from Gauge Origami
The gauge-origami folded instanton partition function yields the characteristic polynomial whose large-x expansion reproduces the commuting Hamiltonians of the elliptic double Calogero-Moser system.