Abstract
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the SD−1 spatial slice in radial quantization in D = 2, 3 dimensions. In each case, we use the conformal Ward Identities to solve systematically for the Fourier components. We then use these Fourier components to build conformal blocks for the four-point function in momentum space, giving a finite-volume version of the momentum-space conformal blocks. We check that this construction is consistent with the known result in infinite volume. Our construction may help to find bootstrap equations that can give nontrivial constraints that do not appear in analysis in infinite volume. We show some examples of bootstrap equations and their nontriviality.
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Acknowledgments
The author thanks his supervisor Simeon Hellerman for his scientific advice. His insight into conformal bootstrap methods helped the author a lot. And the author also thanks their dear schoolmates for providing helpful guidance on research activities.
This project is supported by the WINGS-FMSP (World-leading Innovative Graduate Study for Frontiers of Mathematical Sciences and Physics) project.
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Nishikawa, K. Conformal bootstrap in momentum space at finite volume. J. High Energ. Phys. 2023, 152 (2023). https://doi.org/10.1007/JHEP06(2023)152
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DOI: https://doi.org/10.1007/JHEP06(2023)152