Holography and defect conformal field theories

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS₅×S⁵ bisected by an AdS₄×S² ``brane,'' is dual to N=4 super Yang-Mills theory in R⁴ coupled to an R³ defect. We propose a complete Lagrangian for the field theory dual, a novel ``defect superconformal field theory'' wherein a subset of the fields of N=4 SYM theory interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS₄×S² leads to towers of short representations of $OSp(4|4),$ and we construct the map to a set of dual gauge-invariant defect operators O₃ possessing integer conformal dimensions. Gravity calculations of 〈O₄〉 and 〈O₄O₃〉 are given. Spacetime and N dependence matches expectations from DCFT, while the behavior as functions of λ=g²N at strong and weak coupling is generically different. We comment on a class of correlators for which a nonrenormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a $U(1)$ gauge group. Some weak coupling arguments which illuminate the duality are presented.