2019/10/31 by Andrea Manenti
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computation #Cosmology and Gravitation Theories #Covariant transformation #Differential form #Differential operator #Formalism (music) #Mathematical physics #Mathematics #Multiplet #Operator (biology) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Superfield #Superspace #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep04(2020)145
published as J. High Energ. Phys. 2020, 145 (2020) · Fixed typos in Table 2 and Figure 2
openalex publication_date 2020/04/01 · arxiv created 2020/07/31 · arxiv updated 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A bstract We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 multiplets and some cases of interest for N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2. As an application of the formalism we prove that certain N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 spinning chiral operators (also known as “exotic” chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of three- point functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace.