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The Hamilton-Jacobi method in holography has produced important results bothat a renormalization group (RG) fixed point and away from it. In this paper weuse the Hamilton-Jacobi method to compute the holographic trace anomaly forfour- and six-dimensional boundary conformal field theories (CFTs), assuminghigher-derivative gravity and interactions of scalar fields in the bulk. Thescalar field contributions to the anomaly appear in CFTs with exactly marginaloperators. Moving away from the fixed point, we show that the Hamilton-Jacobiformalism provides a deep connection between the holographic and the local RG.We derive the local RG equation holographically, and verify explicitly that itsatisfies Weyl consistency conditions stemming from the commutativity of Weylscalings. We also consider massive scalar fields in the bulk corresponding toboundary relevant operators, and comment on their effects to the local RGequation.

Holographic Trace Anomaly and Local Renormalization Group