A handbook of holographic 4-point functions

We present a comprehensive discussion of tree-level holographic $4$-point functions scalar operators in momentum space. show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus valid correlator. When $\beta = \Delta - d/2$ are half-integral, with $\Delta$ dimensions $d$ spacetime dimension, diagrams can be evaluated closed form we explicit formulae for case $d=3$ $\Delta=2,3$. These correlators require renormalization, which carry out explicitly, lead to new anomalies beta functions. Correlators different dimension may linked via weight-shifting operators, allow generated from given `seed' correlators. derivation space uncover several subtleties associated their use: such map exchange linear combination contact diagrams, special care must taken when renormalization required.