In this talk I will present a method of derivation of previously known
and new integrable finite difference operators using N=1 quantum field theories. I will start with brief review of the 4d compactifications of 6d SCFTs
leading to the wide class of 4d SCFTs. Then I will show how to derive various finite difference operators using superconformal indices of this 4d theories as well as some intuition coming from the geometry of 6d compactifications. The talk is based on the preprint 2106.08335 as well as ongoing work in collaboration with Shlomo Razamat and Belal Nazzal.