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

Regenerative approaches for V/UHTS feeder links: system analysis and on-board complexity reduction

The dramatically increasing demand for high data rates necessitates the proper dimensioning of the feeder links of very or ultra high throughput satellite (V/UHTS) systems. However, because most of the current solutions rely on transparent payloads, the deployment of a very large number of spatially separated ground stations is necessary to support the total system bandwidth by enabling a full reuse of the scarce available uplink bandwidth. This approach has a significant impact on the complexity and the costs of the ground segment infrastructure. Regenerative payloads could be considered to avoid this design bottleneck. By allowing demodulation and decoding on-board the satellite, the favourable link budget conditions of feeder links compared to the user links can be exploited. Using a spectral efficient transmission technique, the number of ground stations required to support a target sum throughput can be notably reduced. Meanwhile, regenerative solutions have until now barely been used in V/UHTS payloads due to their high on-board power consumption. As a consequence, candidate solutions are proposed in this work to overcome this limitation. A non-coherent modulation technique, known as Differential Amplitude Phase Shift Keying (DAPSK), is introduced to avoid on-board carrier synchronization. Moreover, polar codes are considered to minimize the power consumption of the channel decoder. A preliminary analysis of the expected on-board power consumption compared to that of a standard DVB-S2 approach is conducted using available results in the open literature. Link performance is also evaluated via numerical simulations

Non-Linear Algebra and Bogolubov's Recursion

Numerous examples are given of application of Bogolubov's forest formula to iterative solutions of various non-linear equations: one and the same formula describes everything, from ordinary quadratic equation to renormalization in quantum field theory.Comment: LaTex, 21 page

Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation

Equations related to the Polchinski version of the exact renormalisation group equations for scalar fields which extend the local potential approximation to first order in a derivative expansion, and which maintain reparameterisation invariance, are postulated. Reparameterisation invariance ensures that the equations determine the anomalous dimension eta unambiguously and the equations are such that the result is exact to O(epsilon^2) in an epsilon-expansion for any multi-critical fixed point. It is also straightforward to determine eta numerically. When the dimension d=3 numerical results for a wide range of critical exponents are obtained in theories with O(N) symmetry, for various N and for a ranges of eta, are obtained within the local potential approximation. The associated eta, which follow from the derivative approximation described here, are found for various N. The large N limit of the equations is also analysed. A corresponding discussion is also given in a perturbative RG framework and scaling dimensions for derivative operators are calculated to first order in epsilon.Comment: 30 pages, 4 figures, version 2 some arguments expanded, additional reference

Spin-stiffness and topological defects in two-dimensional frustrated spin systems

Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large class of Heisenberg frustrated spin systems. They are constructed so that to differ only by their topological properties. The spin-stiffnesses for the two systems of tops are calculated for different temperatures and different sizes of the sample. This allows to investigate the role of topological defects in frustrated spin systems. Comparisons with Renormalization Group results based on a Non Linear Sigma model approach and with the predictions of some simple phenomenological model taking into account the topological excitations are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear in Phys.Rev.

Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday. Final versio

A non perturbative approach of the principal chiral model between two and four dimensions

We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.Comment: 5 pages, 1 figure, Revte

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

Critical Behavior of a General O(n)-symmetric Model of two n-Vector Fields in D=4-2 epsilon

The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed points and critical exponents are calculated up to the one- and two-loop order, resp. (eta in two- and three-loop order). Continuous lines of fixed points and O(n)*O(2) invariant discrete solutions were found. Apart from already known fixed points two new ones were found. One agrees in one-loop order with a known fixed point, but differs from it in two-loop order.Comment: 23 page