On analytic bootstrap for interface and boundary CFT

We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation of motion to the boundary operator expansion. The method presented in this paper is general, and it is illustrated in the context of perturbative Wilson-Fisher theories. In particular, we find constraints on the OPE coefficients for the interface CFT in 4 - E dimensions (upto order O(E-2)) with phi(4)-interactions in the bulk. We also compute the corresponding coefficients for the non-unitary phi(3)-theory in 6 - E dimensions in the presence of a conformal boundary equipped with either Dirichlet or Neumann boundary conditions upto order O(E), or an interface upto order O(root c).

Automated summary

Analytic bootstrap techniques are used to extract CFT data for systems with interfaces or boundaries, constrained further by applying equations of motion to boundary operator expansions. The method is general and illustrated in perturbative Wilson-Fisher theories. Constraints on OPE coefficients for interface CFT in 4 - E dimensions and computations for non-unitary phi(3)-theory in 6 - E dimensions with conformal boundaries/interfaces are presented.