Operator expansions, layer susceptibility and two-point functions in BCFT
Parijat Dey, Tobias Hansen, M. A. Shpot
Abstract
A bstract 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 i ϕ i 〉 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 ( ϵ 2 ). These agree with the known results both in ϵ and large- N expansions.