  It was shown recently that boundary terms of conformal anomalies recover the
universal contribution to the entanglement entropy and also play an important
role in the boundary monotonicity theorem of odd-dimensional quantum field
theories. Motivated by these results, we investigate relationships between
boundary anomalies and the stress tensor correlation functions in conformal
field theories. In particular, we focus on how the conformal Ward identity and
the renormalization group equation are modified by boundary central charges.
Renormalized stress tensors induced by boundary Weyl invariants are also
discussed, with examples in spherical and cylindrical geometries.
