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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.03820 |
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| _version_ | 1866909210705395712 |
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| author | Parisini, Enrico Skenderis, Kostas Withers, Benjamin |
| author_facet | Parisini, Enrico Skenderis, Kostas Withers, Benjamin |
| contents | We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) $n$-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03820 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Ambient Space Formalism Parisini, Enrico Skenderis, Kostas Withers, Benjamin High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) $n$-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography. |
| title | The Ambient Space Formalism |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2312.03820 |