A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model

A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies of a universal shape function. This can be viewed as a 2-dimensional, but non-perturbative analogue of the KNO scaling in QCD. Promoted to a working hypothesis, it allows one to compute the two point functions at ``all'' energy or length scales. In addition, the values of two non-perturbative constants (needed for a parameter-free matching of the perturbative and the non-perturbative regime) are determined exactly.Comment: 9 Pages, Latex, 3 Postscript Figure

Spectral geometry as a probe of quantum spacetime

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity -- the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifshitz gravity, among other approaches to quantum gravity.Comment: 25 pages, 6 figures. Version 2: references to figures added, acknowledgment added

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.Comment: 69 pages, Late

The VLQ Calorimeter of H1 at HERA: A Highly Compact Device for Measurements of Electrons and Photons under Very Small Scattering Angles

In 1998, the detector H1 at HERA has been equipped with a small backward spectrometer, the Very Low Q^2 (VLQ) spectrometer comprising a silicon tracker, a tungsten - scintillator sandwich calorimeter, and a Time-of-Flight system. The spectrometer was designed to measure electrons scattered under very low angles, equivalent to very low squared four - momentum transfers Q^2, and high energy photons with good energy and spatial resolution. The VLQ was in operation during the 1999 and 2000 run periods. This paper describes the design and construction of the VLQ calorimeter, a compact device with a fourfold projective energy read-out, and its performance during test runs and in the experiment.Comment: 32 pages, 25 figures, 2 tables (To be submitted to Nucl. Instrum. Meth. A

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

Observable consequences of quantum gravity: Can light fermions exist?

Any theory of quantum gravity must ultimately be connected to observations. This demand is difficult to be met due to the high energies at which we expect the quantum nature of gravity to become manifest. Here we study, how viable quantum gravity proposals can be restricted by investigating the interplay of gravitational and matter degrees of freedom. Specifically we demand that a valid quantum theory of gravity must allow for the existence of light (compared to the Planck scale) fermions, since we observe these in our universe. Within the effective theory framework, we can thus show that UV completions for gravity are restricted, regardless of the details of the microscopic theory. Specialising to asymptotically safe quantum gravity, we find indications that universes with light fermions are favoured within this UV completion for gravity.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS

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

Physics of Trans-Planckian Gravity

We study the field theoretical description of a generic theory of gravity flowing to Einstein General Relativity in IR. We prove that, if ghost-free, in the weakly coupled regime such a theory can never become weaker than General Relativity. Using this fact, as a byproduct, we suggest that in a ghost-free theory of gravity trans-Planckian propagating quantum degrees of freedom cannot exist. The only physical meaning of a trans-Planckian pole is the one of a classical state (Black Hole) which is described by the light IR quantum degrees of freedom and gives exponentially-suppressed contributions to virtual processes. In this picture Einstein gravity is UV self-complete, although not Wilsonian, and sub-Planckian distances are unobservable in any healthy theory of gravity. We then finally show that this UV/IR correspondence puts a severe constraint on any attempt of conventional Wilsonian UV-completion of trans-Planckian gravity. Specifically, there is no well-defined energy domain in which gravity could become asymptotically weak or safe.Comment: 23 pages, 4 figures, v2: Paper reorganized to improve clarity; additional explanations and references added; version accepted for publication in Phys. Rev.

On the renormalization group flow of f(R)-gravity

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln(R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.Comment: 55 pages, 7 figures, typos corrected, references added, version to appear in Phys. Rev.