On the Wick Rotation of the Four-point Function in Conformal Field Theories

Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and have various properties in the Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. In this thesis, we clarify that at the level of four-point functions, the Euclidean CFT axioms imply the standard quantum field theory axioms such as Osterwalder-Schrader axioms (in Euclidean) and Wightman axioms (in Lorentzian).