140 research outputs found
Quantum spacetime and the renormalization group: Progress and visions
The quest for a consistent theory which describes the quantum microstructure
of spacetime seems to require some departure from the paradigms that have been
followed in the construction of quantum theories for the other fundamental
interactions. In this contribution we briefly review two approaches to quantum
gravity, namely, asymptotically safe quantum gravity and tensor models, based
on different theoretical assumptions. Nevertheless, the main goal is to find a
universal continuum limit for such theories and we explain how coarse-graining
techniques should be adapted to each case. Finally, we argue that although
seemingly different, such approaches might be just two sides of the same coin.Comment: 14 pages, 4 figures, Proceedings of "Progress and Visions in Quantum
Theory in View of Gravity: Bridging foundations of physics and mathematics",
Leipzig, 201
Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order
We study a regularization of the Pauli-Villars kind of the one loop
gravitational divergences in any dimension. The Pauli-Villars fields are
massive particles coupled to gravity in a covariant and nonminimal way, namely
one real tensor and one complex vector. The gauge is fixed by means of the
unusual gauge-fixing that gives the same effective action as in the context of
the background field method. Indeed, with the background field method it is
simple to see that the regularization effectively works. On the other hand, we
show that in the usual formalism (non background) the regularization cannot
work with each gauge-fixing.In particular, it does not work with the usual one.
Moreover, we show that, under a suitable choice of the Pauli-Villars
coefficients, the terms divergent in the Pauli-Villars masses can be corrected
by the Pauli-Villars fields themselves. In dimension four, there is no need to
add counterterms quadratic in the curvature tensor to the Einstein action
(which would be equivalent to the introduction of new coupling constants). The
technique also works when matter is coupled to gravity. We discuss the possible
consequences of this approach, in particular the renormalization of Newton's
coupling constant and the appearance of two parameters in the effective action,
that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E
Consistent irrelevant deformations of interacting conformal field theories
I show that under certain conditions it is possible to define consistent
irrelevant deformations of interacting conformal field theories. The
deformations are finite or have a unique running scale ("quasi-finite"). They
are made of an infinite number of lagrangian terms and a finite number of
independent parameters that renormalize coherently. The coefficients of the
irrelevant terms are determined imposing that the beta functions of the
dimensionless combinations of couplings vanish ("quasi-finiteness equations").
The expansion in powers of the energy is meaningful for energies much smaller
than an effective Planck mass. Multiple deformations can be considered also. I
study the general conditions to have non-trivial solutions. As an example, I
construct the Pauli deformation of the IR fixed point of massless non-Abelian
Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the
couplings of the term F^3 and the four-fermion vertices. Another interesting
application is the construction of finite chiral irrelevant deformations of N=2
and N=4 superconformal field theories. The results of this paper suggest that
power-counting non-renormalizable theories might play a role in the description
of fundamental physics.Comment: 23 pages, 5 figures; reference updated - JHE
One Loop Graviton Self-Energy In A Locally De Sitter Background
The graviton tadpole has recently been computed at two loops in a locally de
Sitter background. We apply intermediate results of this work to exhibit the
graviton self-energy at one loop. This quantity is interesting both to check
the accuracy of the first calculation and to understand the relaxation effect
it reveals. In the former context we show that the self-energy obeys the
appropriate Ward identity. We also show that its flat space limit agrees with
the flat space result obtained by Capper in what should be the same gauge.Comment: 35 pages, plain TeX, 4 Postscript files, uses psfig.sty, revised June
1996 for publication in Physical Review
Master Functional And Proper Formalism For Quantum Gauge Field Theory
We develop a general field-covariant approach to quantum gauge theories.
Extending the usual set of integrated fields and external sources to "proper"
fields and sources, which include partners of the composite fields, we define
the master functional Omega, which collects one-particle irreducible diagrams
and upgrades the usual Gamma-functional in several respects. The functional
Omega is determined from its classical limit applying the usual diagrammatic
rules to the proper fields. Moreover, it behaves as a scalar under the most
general perturbative field redefinitions, which can be expressed as linear
transformations of the proper fields. We extend the Batalin-Vilkovisky
formalism and the master equation. The master functional satisfies the extended
master equation and behaves as a scalar under canonical transformations. The
most general perturbative field redefinitions and changes of gauge-fixing can
be encoded in proper canonical transformations, which are linear and do not mix
integrated fields and external sources. Therefore, they can be applied as true
changes of variables in the functional integral, instead of mere replacements
of integrands. This property overcomes a major difficulty of the functional
Gamma. Finally, the new approach allows us to prove the renormalizability of
gauge theories in a general field-covariant setting. We generalize known
cohomological theorems to the master functional and show that when there are no
gauge anomalies all divergences can be subtracted by means of parameter
redefinitions and proper canonical transformations.Comment: 32 pages; v2: minor changes and proof corrections, EPJ
A Master Functional For Quantum Field Theory
We study a new generating functional of one-particle irreducible diagrams in
quantum field theory, called master functional, which is invariant under the
most general perturbative changes of field variables. The usual functional
Gamma does not behave as a scalar under the transformation law inherited from
its very definition as the Legendre transform of W = ln Z, although it does
behave as a scalar under an unusual transformation law. The master functional,
on the other hand, is the Legendre transform of an improved functional W with
respect to the sources coupled to both elementary and composite fields. The
inclusion of certain improvement terms in W and Z is necessary to make the new
Legendre transform well defined. The master functional behaves as a scalar
under the transformation law inherited from its very definition. Moreover, it
admits a proper formulation, obtained extending the set of integrated fields to
so-called proper fields, which allows us to work without passing through Z, W
or Gamma. In the proper formulation the classical action coincides with the
classical limit of the master functional, and correlation functions and
renormalization are calculated applying the usual diagrammatic rules to the
proper fields. Finally, the most general change of field variables, including
the map relating bare and renormalized fields, is a linear redefinition of the
proper fields.Comment: 38 pages, 1 figure; v2: minor changes and proof corrections, EPJ
Renormalization group and logarithmic corrections to scaling relations in conformal sector of 4D gravity
We study the effective theory of the conformal factor near its infrared
stable fixed point.The renormalization group equations for the effective
coupling constants are found and their solutions near the critical point are
obtained, providing the logarithmic corrections to scaling relations.Some
cosmological applications of the running of coupling constants are briefly
discussed.Comment: 9 pages,LATEX fil
Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization
We employ the exponential parametrization of the metric and a \u201cphysical\u201d gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. \ua9 2016, The Author(s)
Ultraviolet Complete Quantum Gravity
An ultraviolet complete quantum gravity theory is formulated in which vertex
functions in Feynman graphs are entire functions and the propagating graviton
is described by a local, causal propagator. The cosmological constant problem
is investigated in the context of the ultraviolet complete quantum gravity.Comment: 11 pages, no figures. Changes to text. Results remain the same.
References added. To be published in European Physics Journal Plu
Massive gravity as a quantum gauge theory
We present a new point of view on the quantization of the massive
gravitational field, namely we use exclusively the quantum framework of the
second quantization. The Hilbert space of the many-gravitons system is a Fock
space where the one-particle Hilbert
space carries the direct sum of two unitary irreducible
representations of the Poincar\'e group corresponding to two particles of mass
and spins 2 and 0, respectively. This Hilbert space is canonically
isomorphic to a space of the type where is a gauge charge
defined in an extension of the Hilbert space
generated by the gravitational field and some ghosts fields
(which are vector Fermi fields) and (which
are vector field Bose fields.)
Then we study the self interaction of massive gravity in the causal
framework. We obtain a solution which goes smoothly to the zero-mass solution
of linear quantum gravity up to a term depending on the bosonic ghost field.
This solution depends on two real constants as it should be; these constants
are related to the gravitational constant and the cosmological constant. In the
second order of the perturbation theory we do not need a Higgs field, in sharp
contrast to Yang-Mills theory.Comment: 35 pages, no figur
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