Liouville conformal field theories in higher dimensions

Liouville conformal field theories in higher dimensions

Blog Article

Abstract 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 $$ mathcal{Q} $$-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 $$ mathcal{Q} Hoodie $$-curvature.We show that C T is independent of the Q $$ mathcal{Q} $$-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 Left Pulse Grip Incline Control 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.