Composite operators near the boundary

Understand

We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory.

• In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions.
• We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor.
• We apply the formalism to a scalar field theory in $d=3-\epsilon$ dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order.