542 research outputs found
Conformal Field Theory on R x S^3 from Quantized Gravity
Conformal algebra on R x S^3 derived from quantized gravitational fields is
examined. The model we study is a renormalizable quantum theory of gravity in
four dimensions described by a combined system of the Weyl action for the
traceless tensor mode and the induced Wess-Zumino action managing
non-perturbative dynamics of the conformal factor in the metric field. It is
shown that the residual diffeomorphism invariance in the radiation^+ gauge is
equal to the conformal symmetry, and the conformal transformation preserving
the gauge-fixing condition that forms a closed algebra quantum mechanically is
given by a combination of naive conformal transformation and a certain
field-dependent gauge transformation. The unitarity issue of gravity is
discussed in the context of conformal field theory. We construct physical
states by solving the conformal invariance condition and calculate their
scaling dimensions. It is shown that the conformal symmetry mixes the
positive-metric and the negative-metric modes and thus the negative-metric mode
does not appear independently as a gauge invariant state at all.Comment: 42 page
Resummation and Higher Order Renormalization in 4D Quantum Gravity
Higher order renormalization in 4D quantum gravity is carried out using
dimensional regularization with great care concerning the conformal-mode
dependence. In this regularization, resummation can be automatically carried
out without making an assumption like that of David, Distler and Kawai. In this
paper we consider a model of 4D quantum gravity coupled to QED. Resummation
inevitably implies a four-derivative quantum gravity. The renormalizability is
directly checked up to and , where and are the
running coupling constants of QED and the traceless gravitational mode. There
is no other running coupling constant in our model. The conformal mode is
treated exactly, which means it is unrenormalized. It is found that Hathrell's
results are included in our results. As a by-product, it is found that a
higher-order gravitational correction to the beta function of QED is negative.
An advantage of our model is that in the very high-energy regime, it closely
resembles exactly solvable 2D quantum gravity. Thus, we can study physical
states of 4D quantum gravity in this regime in parallel to those of 2D quantum
gravity, which can be described with diffeomorphism invariant composite fields.Comment: 39 pages, minor typo error correcte
A Candidate for Renormalizable and Diffeomorphism Invariant 4D Quantum Theory of Gravity
We present evidence that there is a 4D model that satisfies the conditions of
renormalizability and diffeomorphism invariance simultaneously at the 2-loop
level. The traceless mode is treated perturbatively, while the conformal mode
can be managed exactly. The two conditions constrain the theory strongly and
determine the measure of the gravitational field uniquely. Quantum corrections
of the cosmological constant are computed in part to 3-loop diagrams. The
method to remove the negative-metric states is also discussed from the
viewpoint of diffeomorphism invariance in analogy to the gauge in
spontaneously broken gauge theory. The model may be a candidate for a continuum
version of 4D simplicial quantum geometry realized in recent numerical
simulations.Comment: 33 pages, revised and extended version, to appear in Pog. Theor. Phy
RG Analysis for Quantum Gravity with A Single Dimensionless Coupling
We study the quantum conformal gravity whose dynamics is governed by a single
dimensionless gravitational coupling with negative beta function. Since the
Euler term is not dynamical classically, the constant in front of it is not an
independent coupling. Quantum mechanically, however, it induces the Riegert
conformal-factor dynamics with BRST conformal symmetry representing background
free nature. In this paper, we propose how to handle the Euler term
systematically incorporating such dynamics on the basis of renormalization
group analysis using dimensional regularization. As a non-trivial test of
renormalization, we explicitly calculate the three-loop anomalous dimension of
the cosmological constant operator and show that it agrees with the exact
expression derived using the BRST conformal symmetry. The physical significance
to inflation and CMB is also discussed.Comment: 18 pages, 2 figures, added many sentences and paragraphs to explain
the model more in detail, and corrected an error in the tex
Determination of Gravitational Counterterms Near Four Dimensions from RG Equations
The finiteness condition of renormalization gives a restriction on the form
of the gravitational action. By reconsidering the Hathrell's RG equations for
massless QED in curved space, we determine the gravitational counterterms and
the conformal anomalies as well near four dimensions. As conjectured for
conformal couplings in 1970s, we show that at all orders of the perturbation
they can be combined into two forms only: the square of the Weyl tensor in
dimensions and , where is
the usual Euler density, is the rescaled scalar curvature and
is a finite function of only. The number of the dimensionless
gravitational couplings is also reduced to two. can be determined
order by order in series of , whose first several coefficients are
calculated. It has a universal value of at . The familiar ambiguous
term is fixed. At the limit, the conformal anomaly
just yields the combination , which induces Riegert's
effective action.Comment: 29 pages, minor corrections, a reference added, to appear in
Phys.Rev.
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