58 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
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)
Perturbative quantum gravity with the Immirzi parameter
We study perturbative quantum gravity in the first-order tetrad formalism.
The lowest order action corresponds to Einstein-Cartan plus a parity-odd term,
and is known in the literature as the Holst action. The coupling constant of
the parity-odd term can be identified with the Immirzi parameter of loop
quantum gravity. We compute the quantum effective action in the one-loop
expansion. As in the metric second-order formulation, we find that in the case
of pure gravity the theory is on-shell finite, and the running of Newton's
constant and the Immirzi parameter is inessential. In the presence of fermions,
the situation changes in two fundamental aspects. First, non-renormalizable
logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes
a priori observable, and we find that it is renormalized by a four-fermion
interaction generated by radiative corrections. We compute its beta function
and discuss possible implications. The sign of the beta function depends on
whether the Immirzi parameter is larger or smaller than one in absolute value,
and the values plus or minus one are UV fixed-points (we work in Euclidean
signature). Finally, we find that the Holst action is stable with respect to
radiative corrections in the case of minimal coupling, up to higher order
non-renormalizable interactions.Comment: v2 minor amendment
R^4 counterterm and E7(7) symmetry in maximal supergravity
The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio
Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
In three spacetime dimensions, general relativity drastically simplifies,
becoming a ``topological'' theory with no propagating local degrees of freedom.
Nevertheless, many of the difficult conceptual problems of quantizing gravity
are still present. In this review, I summarize the rather large body of work
that has gone towards quantizing (2+1)-dimensional vacuum gravity in the
setting of a spatially closed universe.Comment: 61 pages, draft of review for Living Reviews; comments, criticisms,
additions, missing references welcome; v2: minor changes, added reference
QED coupled to QEG
We discuss the non-perturbative renormalization group flow of Quantum
Electrodynamics (QED) coupled to Quantum Einstein Gravity (QEG) and explore the
possibilities for defining its continuum limit at a fixed point that would lead
to a non-trivial, i.e. interacting field theory. We find two fixed points
suitable for the Asymptotic Safety construction. In the first case, the
fine-structure constant vanishes at the fixed point and its infrared
("renormalized") value is a free parameter not determined by the theory itself.
In the second case, the fixed point value of the fine-structure constant is
non-zero, and its infrared value is a computable prediction of the theory.Comment: 25 pages, 3 figure
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
We present the full two-loop four-graviton amplitudes in N=4,5,6
supergravity. These results were obtained using the double-copy structure of
gravity, which follows from the recently conjectured color-kinematics duality
in gauge theory. The two-loop four-gluon scattering amplitudes in N=0,1,2
supersymmetric gauge theory are a second essential ingredient. The gravity
amplitudes have the expected infrared behavior: the two-loop divergences are
given in terms of the squares of the corresponding one-loop amplitudes. The
finite remainders are presented in a compact form. The finite remainder for N=8
supergravity is also presented, in a form that utilizes a pure function with a
very simple symbol.Comment: 31 pages, 2 figures, 1 table. v2: minor corrections, and references
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