Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions

Journal Article · 24 October 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.086019 · OSTI ID:2474028

Agarwal, Pulkit ; Brower, Richard C.; Raben, Timothy G. ; Tan, Chung-I

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 noncompact maximal Abelian subgroup of $SO(d,2)$ . Reduction of a conformal field theory four-point amplitudes as functions of cross ratios is shown to be equivalent to enforcing $H$ bi-invariance, i.e., $F\left(hg{h}^{\prime }\right)=F\left(g\right)$ , with $g\in SO(d,2)$ and $H$ an appropriate subgroup. Causality is imposed by introducing appropriate semigroups. Causal zonal spherical functions are constructed, making contact with Minkowski conformal blocks introduced previously. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0015845; SC0019139
• OSTI ID: 2474028
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 8 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English