Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions

Understand

Conformal Field Theory in a Minkowski setting is discussed in an embedding space approach, paying special attention to causality constraints for four-point amplitudes.

• The physics of dilatation and Lorentz boost is emphasized in specifying the non-compact Maximal Abelian subgroup (MASG) of $SO(d,2)$.
• Reduction of a Conformal Field Theory (CFT) four-point amplitudes as functions of cross ratios is shown to be equivalent to enforcing $H$ bi-invariance, i.e., $F(hgh')=F(g)$, with $g\in SO(d,2)$ and $H$ an appropriate subgroup.
• Causality is imposed by introducing appropriate semigroups.