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Operator expansions, layer susceptibility and two-point functions in BCFT

Journal of High Energy Physics volume 2020, Article number: 51 (2020) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function 〈ϕiϕi〉 of the O(N) model at the extraordinary transition in 4 − ϵ dimensional semi-infinite space to order O(ϵ). The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(ϵ2). These agree with the known results both in ϵ and large-N expansions.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20, Uppsala, Sweden

    Parijat Dey & Tobias Hansen

  2. Institute for Condensed Matter Physics, Lviv, 79011, Ukraine

    Mykola Shpot

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  1. Parijat Dey
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  2. Tobias Hansen
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Correspondence to Tobias Hansen.

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Dey, P., Hansen, T. & Shpot, M. Operator expansions, layer susceptibility and two-point functions in BCFT. J. High Energ. Phys. 2020, 51 (2020). https://doi.org/10.1007/JHEP12(2020)051

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Keywords

  • Boundary Quantum Field Theory
  • Conformal Field Theory