Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 354 / 2 / c

Choose the Fefferman--Graham coordinates radial variable fromNear the boundary,Consequently, through $O(Z^2)$,By the holographic dictionary, the leading boundary value of $A_{\tau }$ is the source for charge density. Thus $\mu$ is the dimensionless holographic chemical potential; the coefficient of the normalizable linear term is proportional to the CFT charge density, $\rho =\mu L/(4\pi G)$ with the action normalization and outward-orientation convention used here.

Solved by gpt-5.6-sol high.