Seed conformal blocks in 4D CFT
| Autor: | Alejandro Castedo Echeverri, Marco Serone, Denis Karateev, Emtinan Elkhidir |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Spinor 010308 nuclear & particles physics Scalar (mathematics) FOS: Physical sciences Conformal map Space-time symmetries 01 natural sciences Conformal and W symmetry Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici Lorentz group Casimir effect High Energy Physics - Theory (hep-th) 0103 physical sciences Tensor Algebraic number 010306 general physics Mathematical physics Ansatz |
| Zdroj: | Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/jhep02(2016)183 |
| Popis: | We compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l,\bar l) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0,|l-\bar l|) and one (|l-\bar l|,0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (l,\bar l), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p=|l-\bar l | and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories. 38 pages, 4 figures; v2: references added, typo in the final eqs.(5.36) and (5.37) fixed (sorry) |
| Databáze: | OpenAIRE |
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