Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. show, using two independent methods, that QFT can be written terms of causal commutators. The first derivation uses analyticity properties retarded correlators space. second the largest time equation defining time-ordered product. At four points we show formula depends on same double-commutators as formula. $n$-points, a sum nested advanced For four-point functions, is equivalent to formula, up possible semi-local terms. also Polyakov-Regge expansions associated are related by Fourier transform. In process, prove conformal blocks double-commutator equal cut Witten diagrams. Finally, combining with AdS Cutkosky rules, find complete, bulk unitarity method AdS/CFT