Related papers: Anomalies, Unitarity and Quantum Irreversibility
The methods of the renormalization group and the $\varepsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical…
We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the…
In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly $\Delta a$ has been related to the average null energy. We extend this result to derive a…
The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which…
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume…
The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced…
The anomalous effective action describing the coupling of gravity to a non-abelian gauge theory can be determined by a variational solution of the anomaly equation, as shown by Riegert long ago. It is given by a nonlocal expression, with…
A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It…
The Wilsonian renormalization group (RG) properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity,…
I review my explanation of the irreversibility of the renormalization-group flow in even dimensions greater than two and address new investigations and tests.
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance.…
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…
We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced…
Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient $a$ of the Weyl anomaly, while in odd dimensions to the sphere free energy $F$. In recent work…
We prove the renormalizability of quantum gravity near two dimensions. The successful strategy is to keep the volume preserving diffeomorphism as the manifest symmetry of the theory. The general covariance is recovered by further imposing…
We consider matter fields conformally coupled to a background metric and dilaton and describe in detail a quantization procedure and related renormalization group flow that preserve Weyl invariance. Even though the resulting effective…
We consider ${\cal N}=1$ supersymmetric gauge theories in the conformal window. By applying a suitable matter superfield rescaling and a Weyl-transformation the renormalisation group running (matter and gauge field $Z$-factors) are absorbed…
We use the ambient space construction, in which spacetime is mapped into a special lightcone of a higher dimensional manifold, to derive the integrable terms of the trace anomaly in even dimensions. We argue that the natural topological…
We report on the computation of the effective actions describing the interaction of gravity both for an abelian and a non-abelian gauge theory, mediated by the trace anomaly.
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…