Higher loops in AdS: applications to boundary CFT

The Euclidean Anti-de Sitter (AdS) space provides a natural framework for studying boundary conformal field theory (BCFT). We analyze the conformal boundary conditions of the critical O$(N)$ model in $d=4-\epsilon$ dimensions using the $\epsilon$-expansion, and extract some BCFT observables through higher-loop calculations in AdS. Specifically, in the so-called "ordinary" universality class, we determine the free energy to four-loop order and the one-point function of the lightest O$(N)$ singlet operator to three-loop order. In the symmetry breaking "normal" universality class, we derive the two-loop free energy and compute the leading correction to the one-point function of the lightest O($N$) vector. We apply Pad\'e approximants to extract the corresponding conformal data in three dimensions. In particular, from a suitable dimensional continuation of the free energy in AdS, we obtain estimates for the boundary central charge of the BCFT in $d=3$.