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We show that in boundary CFTs, there exists a one-to-one correspondencebetween the boundary operator expansion of the two-point correlation functionand a power series expansion of the layer susceptibility. This general propertyallows the direct identification of the boundary spectrum and expansioncoefficients from the layer susceptibility and opens a new way for efficientcalculations of two-point correlators in BCFTs. To show how it works we derivean explicit expression for the correlation function $\langle\phi_i\phi^i\rangle$ of the O(N) model at the extraordinary transition in4-$\epsilon$ dimensional semi-infinite space to order $O(\epsilon)$. The bulkoperator product expansion of the two-point function gives access to thespectrum of the bulk CFT. In our example, we obtain the averaged anomalousdimensions of scalar composite operators of the O(N) model to order$O(\epsilon^2)$. These agree with the known results both in $\epsilon$ andlarge-N expansions.

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