Search results for "Renormalization Group"
showing 10 items of 206 documents
Operator product expansion coefficients in the exact renormalization group formalism
2020
We study how to compute the operator product expansion coefficients in the exact renormalization group formalism. After discussing possible strategies, we consider some examples explicitly, within the $\epsilon$-expansions, for the Wilson-Fisher fixed points of the real scalar theory in $d=4-\epsilon$ dimensions and the Lee-Yang model in $d=6-\epsilon$ dimensions. Finally we discuss how our formalism may be extended beyond perturbation theory.
Asymptotically safe Lorentzian gravity.
2011
The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Loren…
Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
2008
We review and extend in several directions recent results on the asymptotic safety approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein-Hilbert truncation, where only the cosmological constant and Newton's constant are retained. In this context we make connection with…
Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”
1999
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].
Polyakov effective action from functional renormalization group equation
2010
We discuss the Polyakov effective action for a minimally coupled scalar field on a two dimensional curved space by considering a non-local covariant truncation of the effective average action. We derive the flow equation for the form factor in $\int\sqrt{g}R c_{k}(\Delta)R$, and we show how the standard result is obtained when we integrate the flow from the ultraviolet to the infrared.
Differential Regularization of a Non-relativistic Anyon Model
1994
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\phi {}^{*} \phi {}^{*} \phi \phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions …
Composite operators in asymptotic safety
2017
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dim…
ON QUANTUM GRAVITY, ASYMPTOTIC SAFETY AND PARAMAGNETIC DOMINANCE
2012
We discuss the conceptual ideas underlying the Asymptotic Safety approach to the nonperturbative renormalization of gravity. By now numerous functional renormalization group studies predict the existence of a suitable nontrivial ultraviolet fixed point. We use an analogy to elementary magnetic systems to uncover the physical mechanism behind the emergence of this fixed point. It is seen to result from the dominance of certain paramagnetic-type interactions over diamagnetic ones. Furthermore, the spacetimes of Quantum Einstein Gravity behave like a polarizable medium with a "paramagnetic" response to external perturbations. Similarities with the vacuum state of Yang-Mills theory are pointed …
Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism in…
2008
We explore the nonperturbative renormalization group flow of quantum Einstein gravity (QEG) on an infinite dimensional theory space. We consider ``conformally reduced'' gravity where only fluctuations of the conformal factor are quantized and employ the local potential approximation for its effective average action. The requirement of ``background independence'' in quantum gravity entails a partial differential equation governing the scale dependence of the potential for the conformal factor which differs significantly from that of a scalar matter field. In the infinite dimensional space of potential functions we find a Gaussian as well as a non-Gaussian fixed point which provides further e…
Cosmology with self-adjusting vacuum energy density from a renormalization group fixed point
2001
Cosmologies with a time dependent Newton constant and cosmological constant are investigated. The scale dependence of $G$ and $\Lambda$ is governed by a set of renormalization group equations which is coupled to Einstein's equation in a consistent way. The existence of an infrared attractive renormalization group fixed point is postulated, and the cosmological implications of this assumption are explored. It turns out that in the late Universe the vacuum energy density is automatically adjusted so as to equal precisely the matter energy density, and that the deceleration parameter approaches $q = -1/4$. This scenario might explain the data from recent observations of high redshift type Ia S…