Liouville conformal field theories in higher dimensions

Tom Levy, Yaron Oz

Research output: Contribution to journalArticlepeer-review


We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background Q-curvature charge and an exponential Liouville-type potential. The theories are non-unitary and conformally invariant. They localize semiclassically on solutions that describe manifolds with a constant negative Q-curvature. We show that C T is independent of the Q-curvature charge and is the same as that of a higher derivative scalar theory. We calculate the A-type Euler conformal anomaly of these theories. We study the correlation functions, derive an integral expression for them and calculate the three-point functions of light primary operators. The result is a higher-dimensional generalization of the two-dimensional DOZZ formula for the three-point function of such operators.

Original languageEnglish
Article number119
JournalJournal of High Energy Physics
Issue number6
StatePublished - 2018


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


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