Holographic calculation of boundary terms in conformal anomaly

Understand

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension.

• The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified.
• In this note we present a holographic calculation of those terms in two different prescriptions for the holographic description of the boundary CFT.
• We stress the role of supersymmetry when discussing the holographic description of ${\cal N}=4$ SYM on a $4$-manifold with boundaries.