We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU ( 3 ) sub-sector of the defect CFT dual to the D3–D5 probe brane system with background gauge field flux, k , valid for k = 2 . The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU ( 3 ) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU ( 2 ) counterpart, the one-point function formula for the SU ( 3 ) sub-sector is of determinant type. We discuss the differences with the SU ( 2 ) case and the challenges in extending the present formula beyond k = 2 .
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