$\mathcal{N}=1$ Liouville SCFT in Four Dimensions

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 non-unitary 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.

24 pages; revised

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Cited by in corpus (7)

• Renormalization and conformal invariance of non-local quantum electrodynamics
• dS${}_2$ Supergravity
• CP-violating super Weyl anomaly
• Non-compact duality, super-Weyl invariance and effective actions
• $\mathcal{N}=1$ Liouville SCFT in Four Dimensions
• Polyakov's confinement mechanism for generalized Maxwell theory
• Odd Dimensional Nonlocal Liouville Conformal Field Theories