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

• Published in: The journal of high energy physics 2016-02, Vol.2016 (2), p.1-22, Article 52
• Main Authors: Buhl-Mortensen, Isak, de Leeuw, Marius, Kristjansen, Charlotte, Zarembo, Konstantin
• Format: Article
• Language: English
• Subjects: 1/N Expansion; AdS-CFT Correspondence; Bethe Ansatz; Chains; Classical and Quantum Gravitation; Determinants; Elementary Particles; Flux; Lattice Integrable Models; Mathematical analysis; Mathematical models; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Strings
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP02(2016)052

A bstract 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.