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On Galilean conformal bootstrap

Bin Chen School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China; Collaborative Innovation Center of Quantum Matter, No.5 Yiheyuan Rd, Beijing 100871, P. R. China; Center for High Energy Physics, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China Peng-xiang Hao Yau Mathematical Sciences Center,Tsinghua University, Beijing, 100084, China Reiko Liu School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China Zhe-Fei Yu School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, No.5 Yiheyuan Rd, Beijing 100871, P. R. China

arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2206.74019

2021.5
In this work, we develop conformal bootstrap for Galilean conformal field theory (GCFT). In a GCFT, the Hilbert space could be decomposed into quasiprimary states and its global descendants. Different from the usual conformal field theory, the quasi-primary states in a GCFT constitute multiplets, which are block-diagonized under the Galilean boost operator. More importantly the multiplets include the states of negative norms, indicating the theory is not unitary. We compute global blocks of the multiplets, and discuss the expansion of four-point functions in terms of the global blocks of the multiplets. Furthermore we do the harmonic analysis for the Galilean conformal symmetry and obtain an inversion formula. As the first step to apply the Galilean conformal bootstrap, we construct generalized Galilean free theory (GGFT) explicitly. We read the data of GGFT by using Taylor series expansion of four-point function and the inversion formula independently, and find exact agreement. We discuss some novel features in the Galilean conformal bootstrap, due to the non-semisimpleness of the Galilean conformal algebra and the non-unitarity of the GCFTs.
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@inproceedings{bin2021on,
  title={On Galilean conformal bootstrap},
  author={Bin Chen, Peng-xiang Hao, Reiko Liu, and Zhe-Fei Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616160949232516386},
  year={2021},
}
Bin Chen, Peng-xiang Hao, Reiko Liu, and Zhe-Fei Yu. On Galilean conformal bootstrap. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616160949232516386.
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