Abstract
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.
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Acknowledgments
It is a pleasure to thank Federico Capone, Matthew Dodelson, Kara Farnsworth, Robin Graham, Andrei Parnachev, Nicole Righi and Jakob Salzer for discussions. The work of EP is supported by the Royal Society Research Grants RGF/EA/181054 and RF/ERE/210267. KS and BW are supported in part by the Science and Technology Facilities Council (Consolidated Grant “Exploring the Limits of the Standard Model and Beyond”). BW is supported by a Royal Society University Research Fellowship.
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Parisini, E., Skenderis, K. & Withers, B. The ambient space formalism. J. High Energ. Phys. 2024, 296 (2024). https://doi.org/10.1007/JHEP05(2024)296
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DOI: https://doi.org/10.1007/JHEP05(2024)296