N= 1 Liouville SCFT in four dimensions

Tom Levy*, Yaron Oz, Avia Raviv-Moshe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 Q-curvature charge and an exponential potential. It localizes semiclassically on solutions that describe curved superspaces with a constant complex supersymmetric 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.

Original languageEnglish
Article number122
JournalJournal of High Energy Physics
Issue number12
StatePublished - 1 Dec 2018


FundersFunder number
Alexander Zaks Scholarship
ISF Center of Excellence
US-Israel Binational Science Foundation
German-Israeli Foundation for Scientific Research and Development
Israel Academy of Sciences and Humanities
Planning and Budgeting Committee of the Council for Higher Education of Israel1937/12


    • Anomalies in Field and String Theories
    • Conformal Field Theory
    • Field Theories in Higher Dimensions
    • Supergravity Models


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