Distributions in CFT. Part II. Minkowski space

A bstract CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent OPE. It is nowadays common to assume that CFT correlators exist and have various properties also Lorentzian signature. Some of these may represent extra assumptions, it an open question if they hold for familiar statistical-physics critical 3d Ising model. Here we consider Wightman 4-point functions scalar primaries We derive a minimal set their solely from unitary axioms, without using assumptions. establish all axioms (temperedness, spectral property, local commutativity, clustering), conformal invariance, distributional convergence s-channel This done constructively, by analytically continuing OPE expansion radial cross-ratios ρ , $$ \overline{\rho} ρ ¯ . prove key fact | |, \left|\overline{\rho}\right| < 1 inside forward tube, bounds on how fast tend when approaching Minkowski space. provide guide axiomatic QFT literature modern audience. review Osterwalder-Schrader (OS) QFTs, celebrated OS theorem connecting them. classic result Mack about convergence. arguments turn out useful our setup. Others fall short needs due assumptions (Mack) or unverifiable (OS theorem).