The dual of Janus -:- an interface CFT

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value <L'> are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, <T_{\mu\nu}>=0, and this is confirmed in first order in the discontinuity.