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arXiv · 2302.06469

Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions

Pulkit Agarwal·Richard C. Brower·Timothy G. Raben·Chung-I Tan
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Abstract

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. Causal zonal spherical functions are constructed, making contact with Minkowski conformal blocks introduced previously.

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Pulkit Agarwal, Richard C. Brower, Timothy G. Raben, Chung-I Tan. 2023-02-13. Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions. https://arxiv.org/abs/2302.06469

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