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 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 mathcal{Q} -curvature. We show that CT is independent of the 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 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.
Highlights
Background chargeFor a conformally flat manifold with the topology of the sphere we get using (2.3) for a constant shift of the field by φ0: SC.G.(φ + φ0, g) = SC.G.(φ, g) + dQφ0 . (2.10)We will study these theories on the d-sphere Sd and the following discussion is a generalization of the two-dimensional analysis in [14] to d-dimensions
We study the correlation functions, derive an integral expression for them and calculate the three-point functions of light primary operators
This is the higher-dimensional generalization of the two-dimensional DOZZ formula for the three-point function of light primary operators [13, 14]
Summary
There are two objects in the action (1.1) that play an important role in conformal geometry (for a review see e.g. [15]). There are two objects in the action (1.1) that play an important role in conformal geometry The first are the conformally covariant GJMS operators Pg [9]. In two and four dimensions they are the Laplacian and the Paneitz operator [16], respectively: Pd=2 = − , Pd=4 = ∇a. The second object is the Q-curvature Qg [10], that takes in two and four dimensions the form: Qd=2. The integral of the Q-curvature on a Riemannian manifold M is an invariant of the conformal structure, but is not in general a topological invariant. When M is a conformally flat manifold, the Q-curvature is related to the Euler density Ed and: M ddx√gQg. where χ(M ) is the Euler characteristic of M
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
