21 research outputs found
Back reaction of vacuum and the renormalization group flow from the conformal fixed point
We consider the GUT-like model with two scalar fields which has infinitesimal
deviation from the conformal invariant fixed point at high energy region. In
this case the dominating quantum effect is the conformal trace anomaly and the
interaction between the anomaly-generated propagating conformal factor of the
metric and the usual dimensional scalar field. This interaction leads to the
renormalization group flow from the conformal point. In the supersymmetric
conformal invariant model such an effect produces a very weak violation of
sypersymmetry at lower energies.Comment: 15 pages, LaTex, ten figures, uuencoded fil
Search for flow invariants in even and odd dimensions
A flow invariant in quantum field theory is a quantity that does not depend
on the flow connecting the UV and IR conformal fixed points. We study the flow
invariance of the most general sum rule with correlators of the trace Theta of
the stress tensor. In even (four and six) dimensions we recover the results
known from the gravitational embedding. We derive the sum rules for the trace
anomalies a and a' in six dimensions. In three dimensions, where the
gravitational embedding is more difficult to use, we find a non-trivial
vanishing relation for the flow integrals of the three- and four-point
functions of Theta. Within a class of sum rules containing finitely many terms,
we do not find a non-vanishing flow invariant of type a in odd dimensions. We
comment on the implications of our results.Comment: 21 pages, v2: expanded introduction, published in NJ
A note on the improvement ambiguity of the stress tensor and the critical limits of correlation functions
I study various properties of the critical limits of correlators containing
insertions of conserved and anomalous currents. In particular, I show that the
improvement term of the stress tensor can be fixed unambiguously, studying the
RG interpolation between the UV and IR limits. The removal of the improvement
ambiguity is encoded in a variational principle, which makes use of sum rules
for the trace anomalies a and a'. Compatible results follow from the analysis
of the RG equations. I perform a number of self-consistency checks and discuss
the issues in a large set of theories.Comment: 15 page
Renormalization Ambiguities and Conformal Anomaly in Metric-Scalar Backgrounds
We analyze the problem of the existing ambiguities in the conformal anomaly
in theories with external scalar field in curved backgrounds. In particular, we
consider the anomaly of self-interacting massive scalar field theory and of
Yukawa model in the massless conformal limit. In all cases the ambiguities are
related to finite renormalizations of a local non-minimal terms in the
effective action. We point out the generic nature of this phenomenon and
provide a general method to identify the theories where such an ambiguity can
arise.Comment: RevTeX, 10 pages, no figures. Small comment and two references added.
Accepted for publication in Physical Review
Twenty Years of the Weyl Anomaly
In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered
that the conformal invariance under Weyl rescalings of the metric tensor
displayed by classical
massless field systems in interaction with gravity no longer survives in the
quantum theory. Since then these Weyl anomalies have found a variety of
applications in black hole physics, cosmology, string theory and statistical
mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest},
ICTP, Trieste, March 1993.)Comment: 43 page
Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT
We study the renormalizable quantum gravity formulated as a perturbed theory
from conformal field theory (CFT) on the basis of conformal gravity in four
dimensions. The conformal mode in the metric field is managed
non-perturbatively without introducing its own coupling constant so that
conformal symmetry becomes exact quantum mechanically as a part of
diffeomorphism invariance. The traceless tensor mode is handled in the
perturbation with a dimensionless coupling constant indicating asymptotic
freedom, which measures a degree of deviation from CFT. There are no massive
ghosts because they are not gauge invariant in this formulation. Higher order
renormalization is carried out using dimensional regularization, in which the
Wess-Zumino integrability condition is applied to reduce indefiniteness
existing in higher-derivative actions. The effective action of quantum gravity
improved by renormalization group is obtained. We then make clear that
conformal anomalies are indispensable quantities to preserve diffeomorphism
invariance. Anomalous scaling dimensions of the cosmological constant and the
Planck mass are calculated. The effective cosmological constant is obtained in
the large number limit of matter fields.Comment: 51 pages, 12 figure