One Loop Beta Functions in Topologically Massive Gravity

We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point.Comment: 44 pages, 16 figure

Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario

We investigate the high-energy properties of matter theories coupled to quantum gravity. Specifically, we show that quantum gravity fluctuations generically induce matter self-interactions in a scalar theory. Our calculations apply within asymptotically safe quantum gravity, where our results indicate that the UV is dominated by an interacting fixed point, with non-vanishing gravitational as well as matter couplings. In particular, momentum-dependent scalar self-interactions are non-zero and induce a non-vanishing momentum-independent scalar potential. Furthermore we point out that terms of this type can have observable consequences in the context of scalar-field driven inflation, where they can induce potentially observable non-Gaussianities in the CMB.Comment: 15 + 8 pages, 8 figures, extended truncation, version to be published in PR

Asymptotic Safety, Emergence and Minimal Length

There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.Comment: LaTEX, 20 pages, 2 figures; v.2: minor changes, reflecting published versio

Renormalization Group Flow in Scalar-Tensor Theories. II

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.Comment: 14 pages. v.2: Minor changes, some references adde

Search of scaling solutions in scalar-tensor gravity

We write new functional renormalization group equations for a scalar nonminimally coupled to gravity. Thanks to the choice of the parametrization and of the gauge fixing they are simpler than older equations and avoid some of the difficulties that were previously present. In three dimensions these equations admit, at least for sufficiently small fields, a solution that may be interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also find for any dimension d>2 two analytic scaling solutions which we study for d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert truncation, the others involve a nonvanishing minimal coupling

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)

The background scale Ward identity in quantum gravity

We show that with suitable choices of parametrization, gauge fixing and cutoff, the anomalous variation of the effective action under global rescalings of the background metric is identical to the derivative with respect to the cutoff, i.e. to the beta functional, as defined by the exact RG equation. The Ward identity and the RG equation can be combined, resulting in a modified flow equation that is manifestly invariant under global background rescalings

Computing the effective action with the functional renormalization group

The \u201cexact\u201d or \u201cfunctional\u201d renormalization group equation describes the renormalization group flow of the effective average action \u393 k. The ordinary effective action \u393 0 can be obtained by integrating the flow equation from an ultraviolet scale k= \u39b down to k= 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang\u2013Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. \ua9 2016, The Author(s)

New Approach to GUTs

We introduce a new string-inspired approach to the subject of grand unification which allows the GUT scale to be small, \lesssim 200 TeV, so that it is within the reach of {\em conceivable} laboratory accelerated colliding beam devices. The key ingredient is a novel use of the heterotic string symmetry group physics ideas to render baryon number violating effects small enough to have escaped detection to date. This part of the approach involves new unknown parameters to be tested experimentally. A possible hint at the existence of these new parameters may already exist in the EW precision data comparisons with the SM expectations.Comment: 8 pages; improved text and references, note added; extended text, 1 figure added; extended text for publication in Eur. Phys. Journal

On the scheme dependence of gravitational beta functions

We discuss the arbitrariness in the choice of cutoff scheme in calculations of beta functions. We define a class of "pure" cutoff schemes, in which the cutoff is completely independent of the parameters that appear in the action. In a sense they are at the opposite extreme of the "spectrally adjusted" cutoffs, which depend on all the parameters that appear in the action. We compare the results for the beta functions of Newton's constant and of the cosmological constant obtained with a typical cutoff and with a pure cutoff, keeping all else fixed. We find that the dependence of the fixed point on an arbitrary parameter in the pure cutoff is rather mild. We then show in general that if a spectrally adjusted cutoff produces a fixed point, there is a corresponding pure cutoff that will give a fixed point in the same position