One-point functions in AdS/dCFT from matrix product states
2016 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 2, 052Article in journal (Refereed) PublishedText
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.
Place, publisher, year, edition, pages
2016. no 2, 052
AdS-CFT Correspondence, Bethe Ansatz, Lattice Integrable Models, 1/N Expansion
IdentifiersURN: urn:nbn:se:uu:diva-280254DOI: 10.1007/JHEP02(2016)052ISI: 000370001200001OAI: oai:DiVA.org:uu-280254DiVA: diva2:910522
FunderEU, FP7, Seventh Framework Programme, 317089EU, European Research Council, 341222Swedish Research Council, 2013-4329