Pawel O. Mazur

Weyl cohomology and the effective action for conformal anomalies

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistency condition by construction. The method relies on defining the coboundary operator of the local Weyl group,

The path integral measure, conformal factor problem and stability of the ground state of quantum gravity

{g}_{\mathrm{ab}}\ensuremath{\rightarrow}\mathrm{exp}(2\ensuremath{\sigma}{)g}_{\mathrm{ab}},

SU(3) extension of the skyrme model

and giving a cohomological interpretation to counterterms in the effective action in dimensional regularization with respect to this group. Nontrivial cocycles of the Weyl group arise from local functionals that are Weyl invariant in and only in the physical even integer dimension

Cosmological dark energy: prospects for a dynamical theory

d=2k.

Conformal Invariance, Dark Energy, and CMB Non-Gaussianity

In the physical dimension the nontrivial cocycles generate covariant nonlocal action functionals characterized by sensitivity to global Weyl rescalings. The nonlocal action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings. These distinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the

Conformal Invariance and Cosmic Background Radiation

d=4

Conformal symmetry and central charges in 4 dimensions

nonlocal effective action yields two new conserved geometric stress tensors with local traces equal to the square of the Weyl tensor and the Gauss-Bonnet-Euler density, respectively. The second of these conserved tensors becomes

Physical states of the quantum conformal factor

{}^{(3)}{H}_{\mathrm{ab}}

Tommy Gold Revisited: Why Doesn’t the Universe Rotate?

in conformally flat spaces, exposing the previously unsuspected origin of this tensor. The method may be extended to any even dimension by making use of the general construction of conformal invariants given by Fefferman and Graham. As a corollary, conformal field theory (CFT) behavior of correlators at the asymptotic infinity of either anti\char21{}de Sitter or de Sitter spacetimes follows, i.e.,

Criticality and scaling in 4D quantum gravity

{\mathrm{AdS}}_{d+1}\ensuremath{-}