Abstract
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 − ϵ dimensions (upto order mathcal{O} (ϵ2)) with ϕ4-interactions in the bulk. We also compute the corresponding coefficients for the non-unitary ϕ3-theory in 6 − ϵ dimensions in the presence of a conformal boundary equipped with either Dirichlet or Neumann boundary conditions upto order mathcal{O} (ϵ), or an interface upto order mathcal{O}left(sqrt{epsilon}right) .
Highlights
A conformal transformation, which corresponds to an interface communicating with the two CFTs
They can still provide information about the bulk CFTs. These theories contain both the bulk operators as well as operators living on the boundary or the interface, and allow CFT techniques to be extended to a larger domain in the space of QFTs
Exploiting the analytic properties of the bulk and boundary conformal blocks we have shown how to extract the
Summary
We discuss the analytic structure of the conformal blocks in a CFT with a boundary. Let us look into the analytic structure of the bulk and boundary conformal blocks Gope and Gboe. Both of the blocks in (2.4) have a branch cut at ξ < 0 that originates from generic non-integer power of ξ. The discontinuity of the bulk block at ξ < −1 for the bulk exchange of double-trace operators of dimension ∆ = d − 2 + 2n can be expressed in terms of Jacobi polynomials (this holds for any d) disc Gope(d ξ
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