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We develop both the gravity and field theory sides of the Karch-Randallconjecture that the near-horizon description of a certain D5-D3 braneconfiguration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 xS^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3defect. 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 SYMinteracts with a d=3 SU(N) fundamental hypermultiplet on the defect preservingconformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrappedD5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4),and we construct the map to a set of dual gauge-invariant defect operators O_3possessing integer conformal dimensions. Gravity calculations of <O_4> and<O_4O_3> are given. Spacetime and N-dependence matches expectations from dCFT,while the behavior as functions of lambda = g^2 N at strong and weak couplingis generically different. We comment on a class of correlators for which anon-renormalization theorem may still exist. Partial evidence for theconformality of the quantum theory is given, including a complete argument forthe special case of a U(1) gauge group. Some weak coupling arguments whichilluminate the duality are presented.Comment: 47 pages, LaTeX, 2 figures, feynmf. v2: fixed minor errors, added  references. v3: fixed more typo

Holography and defect conformal field theories