The paper by Minahan and Zarembo derives the one-loop mixing matrix for anomalous dimensions in $\mathcal{N} = 4$ Super Yang-Mills (SYM). They show that this matrix can be identified with the Hamiltonian of an integrable $SO(6)$ spin chain with vector sites. Using the Bethe ansatz, they provide a recipe to compute anomalous dimensions for a wide range of operators, including exact results for BMN operators with two impurities and results up to first-order $1/J$ corrections for BMN operators with many impurities. They also use Reshetikhin's result to find the exact one-loop anomalous dimension for an $SO(6)$ singlet in the limit of large bare dimension, showing that this anomalous dimension is proportional to the square root of the string level in the weak coupling limit. The paper discusses the application of the Bethe ansatz to various scenarios, including the addition of multiple impurities and the computation of anomalous dimensions for operators outside the BMN limit.The paper by Minahan and Zarembo derives the one-loop mixing matrix for anomalous dimensions in $\mathcal{N} = 4$ Super Yang-Mills (SYM). They show that this matrix can be identified with the Hamiltonian of an integrable $SO(6)$ spin chain with vector sites. Using the Bethe ansatz, they provide a recipe to compute anomalous dimensions for a wide range of operators, including exact results for BMN operators with two impurities and results up to first-order $1/J$ corrections for BMN operators with many impurities. They also use Reshetikhin's result to find the exact one-loop anomalous dimension for an $SO(6)$ singlet in the limit of large bare dimension, showing that this anomalous dimension is proportional to the square root of the string level in the weak coupling limit. The paper discusses the application of the Bethe ansatz to various scenarios, including the addition of multiple impurities and the computation of anomalous dimensions for operators outside the BMN limit.