AdS scalar-field boundary asymptotics
= AdS scalar-field boundary asymptotics
A scalar field of mass $m$ in $\operatorname{AdS}_{d+1}$ behaves near the conformal boundary as $\phi=z^{d-\Delta}J+z^\Delta A+\cdots$, where $m^2=\Delta(\Delta-d)$. The leading coefficient is the source and the normalizable coefficient determines the operator expectation value.