General bootstrap equations in 4D CFTs. We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of $n$-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Finally, we implement our framework in a Mathematica package and make it freely available.

References in zbMATH (referenced in 32 articles , 1 standard article )

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  1. Hoback, Sarah; Parikh, Sarthak: Towards Feynman rules for conformal blocks (2021)
  2. Silva, Joao A.: Four point functions in CFT’s with slightly broken higher spin symmetry (2021)
  3. Burić, Ilija; Schomerus, Volker; Isachenkov, Mikhail: Conformal group theory of tensor structures (2020)
  4. Burić, Ilija; Schomerus, Volker; Sobko, Evgeny: Superconformal blocks: general theory (2020)
  5. Cuomo, Gabriel: Superfluids, vortices and spinning charged operators in 4d CFT (2020)
  6. Fortin, Jean-François; Ma, Wen-Jie; Skiba, Witold: Higher-point conformal blocks in the comb channel (2020)
  7. Fortin, Jean-François; Prilepina, Valentina; Skiba, Witold: Conformal two-point correlation functions from the operator product expansion (2020)
  8. Fortin, Jean-François; Prilepina, Valentina; Skiba, Witold: Conformal four-point correlation functions from the operator product expansion (2020)
  9. Fortin, Jean-François; Skiba, Witold: New methods for conformal correlation functions (2020)
  10. Liendo, Pedro; Linke, Yannick; Schomerus, Volker: A Lorentzian inversion formula for defect CFT (2020)
  11. Manenti, Andrea: Differential operators for superconformal correlation functions (2020)
  12. Parikh, Sarthak: A multipoint conformal block chain in (d) dimensions (2020)
  13. Binder, Damon J.; Chester, Shai M.; Pufu, Silviu S.; Wang, Yifan: (\mathcalN= 4) super-Yang-Mills correlators at strong coupling from string theory and localization (2019)
  14. Elkhidir, Emtinan; Karateev, Denis: Scalar-fermion analytic bootstrap in 4D (2019)
  15. Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr: Recursion relation for general 3d blocks (2019)
  16. Karateev, Denis; Kravchuk, Petr; Serone, Marco; Vichi, Alessandro: Fermion conformal bootstrap in 4d (2019)
  17. Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David: Harmonic analysis and mean field theory (2019)
  18. Ramírez, Israel A.: Towards general super Casimir equations for $4D$ $ \mathcalN=1 $ SCFTs (2019)
  19. Rosenhaus, Vladimir: Multipoint conformal blocks in the comb channel (2019)
  20. Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan; Wang, Yifan: Spheres, charges, instantons, and bootstrap: a five-dimensional odyssey (2018)

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