Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 354 / 2 / b / ii / Solution

The divergence is local in the induced boundary metric and is cancelled by the leading holographic renormalization countertermOn the regulated cylinder this iswhich cancels the ${ϵ}^{-2}$ divergence of $I_{\mathrm{GR}}$. An overall sign changes if one uses the oppositely signed Euclidean generating functional; the local counterterm changes with it.