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

Authors: Parijat Dey, Tobias Hansen, Mykola Shpot

Preprint number: UUITP-21/20

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 <ϕ_iϕⁱ> of the O(N) model at the extraordinary transition in 4-epsilon 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 epsilon and large-N expansions.