Constructing CFTs from AdS flows

We study the renormalization group flow equations for correlation functions of weakly coupled quantum field theories in AdS. Taking limit where external points approach conformal boundary, we obtain a conformally invariant functions. solve one- and two-point show that corrections to dimensions can be obtained as an integral over Mellin amplitude four-point function. also derive higher $n$-point then consider flows at tree level one loop (in AdS), obtains exactly recursion relations corresponding amplitudes derived earlier by Fitzpatrick et al. [arXiv:1107.1499] Yuan [arXiv:1710.01361,arXiv:1801.07283] loop. As application, furthermore compute one-loop some operators CFT dual $\mathrm{O}(N)$ scalar model