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General bootstrap equations in 4D CFTs. (English) Zbl 1384.81094

Summary: 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.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
81T55 Casimir effect in quantum field theory
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