N = 2 Liouville SCFT in four dimensions

Tom Levy*, Yaron Oz, Avia Raviv-Moshe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We construct a Liouville superconformal field theory with eight real supercharges in four dimensions. The Liouville superfield is an 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 N = 2 superspace and analyze them in the semiclassical approximation by using a quaternionic formalism for the N = 2 superconformal algebra.

Original languageEnglish
Article number6
JournalJournal of High Energy Physics
Issue number10
StatePublished - 1 Oct 2019


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


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