One-point Functions in AdS/dCFT from Matrix Product States

Understand

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 prefactor.
• 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.