Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929496706252800 |
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| author | Agarwal, Pulkit Brower, Richard C. Raben, Timothy G. Tan, Chung-I |
| author_facet | Agarwal, Pulkit Brower, Richard C. Raben, Timothy G. Tan, Chung-I |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06469 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions Agarwal, Pulkit Brower, Richard C. Raben, Timothy G. Tan, Chung-I High Energy Physics - Theory 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. |
| title | Embedding Space Approach to Lorentzian CFT Amplitudes and Causal Spherical Functions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2302.06469 |