Orateur
Description
We found that in boundary conformal field theories, 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 a 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 $\langle\phi_i \phi^i\rangle$ of the $O(n)$ model at the extraordinary transition in $4-\varepsilon$ dimensional semi-infinite space to order $O(\varepsilon)$.
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 $O(\varepsilon^2)$. These agree with the known results both in $\varepsilon$ and large-$n$ expansions.
