Article open access publication

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

Journal of High Energy Physics, Springer Nature, ISSN 1126-6708

Volume 2016, 2, 2016

DOI:10.1007/jhep02(2016)052, Dimensions: pub.1043579163,

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  1. (1) University of Copenhagen, grid.5254.6, KU
  2. (2) Stockholm University, grid.10548.38
  3. (3) Uppsala University, grid.8993.b

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Denmark

Sweden

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Europe

Description

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.

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Times Cited: 41

Field Citation Ratio (FCR): 38.6

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