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We study Baxter's T-Q equation of XXX spin-chain models under thesemiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondenceemerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theorieshaving the above different gauge groups are encoded simultaneously in oneBaxter's T-Q equation which captures their spectral curves. For example, whileone is SU(N_c) with N_f=2N_c flavors the other turns out to be SU(2)^{N_c-3}with N_c hyper-multiplets (N_c > 3). It is seen that the correspondingSeiberg-Witten differential supports our proposal.

Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and \Omega-deformed Seiberg-Witten prepotential