Abstract
We construct a four supercharges Liouville superconformal field theory in four dimensions. The Liouville superfield is chiral and its lowest component is a log-correlated complex scalar whose real part carries a background charge. The action consists of a supersymmetric Paneitz operator, a background supersymmetric \( \mathcal{Q} \)-curvature charge and an exponential potential. It localizes semiclassically on solutions that describe curved superspaces with a constant complex supersymmetric \( \mathcal{Q} \)-curvature. The theory is nonunitary with a continuous spectrum of scaling dimensions. We study the dynamics on the supersymmetric 4-sphere, show that the classical background charge is not corrected quantum mechanically and calculate the super-Weyl anomaly. We derive an integral form for the correlation functions of vertex operators.
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Levy, T., Oz, Y. & Raviv-Moshe, A. \( \mathcal{N}=1 \) Liouville SCFT in four dimensions. J. High Energ. Phys. 2018, 122 (2018). https://doi.org/10.1007/JHEP12(2018)122
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DOI: https://doi.org/10.1007/JHEP12(2018)122