One-point functions in AdS/dCFT from matrix product states

One-point functions of certain non-protected scalar operators in the defect cft dual to the d3-d5 probe brane system with k units of world volume flux can be expressed as overlaps between bethe eigenstates of the heisenberg spin chain and a matrix product state. we present a closed expression of determinant form for these one-point functions, valid for any value of k. the determinant formula factorizes into the k = 2 result times a k-dependent pre-factor. making use of the transfer matrix of the heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k = 2 and k = 3 respectively. we furthermore find evidence that the matrix product states for k = 2 and k = 3 are related via a ratio of baxter’s q-operators. the general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. we revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.