Abstract
We construct a Liouville superconformal field theory with eight real supercharges in four dimensions. The Liouville superfield is an \( \mathcal{N} \) = 2 chiral superfield with sixteen bosonic and sixteen fermionic component fields. Its lowest component is a logcorrelated complex scalar field whose real part carries a background charge. The theory is non-unitary with a continuous spectrum of scaling dimensions. We study its quantum dynamics on the supersymmetric 4-sphere and show that the classical background charge is not corrected quantum mechanically. We calculate the super-Weyl anomaly coefficients and find that c vanishes, while a is negative and depends on the background charge. We derive an integral expression for the correlation functions of superfield vertex operators in \( \mathcal{N} \) = 2 superspace and analyze them in the semiclassical approximation by using a quaternionic formalism for the \( \mathcal{N} \) = 2 superconformal algebra.
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ArXiv ePrint: 1907.08961
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Levy, T., Oz, Y. & Raviv-Moshe, A. \( \mathcal{N} \) = 2 Liouville SCFT in four dimensions. J. High Energ. Phys. 2019, 6 (2019). https://doi.org/10.1007/JHEP10(2019)006
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DOI: https://doi.org/10.1007/JHEP10(2019)006