Abstract
We ask when it is possible to construct arbitrary unitary multiplets of the superconformal algebra with eight Poincaré supercharges that are compatible with locality from (continuous deformations of) representations in free field theories. We answer this question in two, three, and five dimensions. In four dimensions, we resort to an intricate but self-consistent web of conjectures. If correct, these conjectures imply various new non-perturbative constraints on short multiplets in any local unitary 4d \( \mathcal{N} \) = 2 superconformal field theory and on an unusual set of related vertex algebras. Throughout, we connect our results with properties of deformations in the space of theories.
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Acknowledgments
We are grateful to A. Banerjee, C. Bhargava, J. Distler, A. Manenti, and S. Razamat for comments and discussions. M. B. and H. J. were supported by the grant “Amplitudes, Strings and Duality” from STFC. M. B. was also supported by the grant “Relations, Transformations, and Emergence in Quantum Field Theory” from the Royal Society. M. B. thanks SISSA and Nordita for hospitality during parts of this project. No new data were generated or analysed during this study.
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Buican, M., Jiang, H. From free fields to interacting SCFTs via representation theory. J. High Energ. Phys. 2024, 230 (2024). https://doi.org/10.1007/JHEP08(2024)230
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DOI: https://doi.org/10.1007/JHEP08(2024)230