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

• Published in: arXiv.org 2015-12
• Main Authors: Buhl-Mortensen, Isak, de Leeuw, Marius, Kristjansen, Charlotte, Zarembo, Konstantin
• Format: Article
• Language: English
• Subjects: Chains; Eigenvectors; Field theory; Operators (mathematics)
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1512.02532

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. 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.