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

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

Rationality of spectral action for Robertson-Walker metrics

We use parametric pseudodifferential calculus to prove a conjecture by A. Connes and A. Chamseddine: we show that each term in the heat kernel expansion of the Dirac-Laplacian of a Robertson-Walker metric is described a several variable polynomial with rational coefficients