Quantum Integrability for Three-Point Functions

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Quantum corrections to three-point functions of scalar single trace operators in planar ${\cal N}=4$ Super-Yang-Mills theory are studied using integrability. At one loop, we find  new algebraic structures that not only govern all two loop corrections to the mixing of the operators but also automatically incorporate all one loop diagrams correcting the tree level Wick contractions. Speculations about possible extensions of our construction to all loop orders are given. We also match our results with the strong coupling predictions in the classical (Frolov-Tseytlin) limit.