Replica-deformation of the SU(2)-invariant Thirring model via solutions of the qKZ equation

The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (`replica') deformation of the form factor approach. We show that replica-deformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational $sl_2$-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether current in our model.Comment: 30 pages, Latex, Dedicated to Moshe Flat

Preferred foliation effects in Quantum General Relativity

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a preferred foliation, described effectively via a scalar field with non-standard dynamics. We find that vanishing Lorentz violation is a UV attractive fixed-point of this model in the local potential approximation. Since larger truncations may lead to differing results, we study as a first example effects of additional matter fields on the RG running of the Lorentz violating term and provide a general argument why they are small.Comment: 12 pages, no figures, compatible with published versio

Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wave-function renormalization of the ghost fields. The latter induces non-trivial corrections to the beta-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point in agreement with the asymptotic safety conjecture, which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 figure

Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model

The two-point functions of the energy-momentum tensor and the Noether current are used to probe the O(3) nonlinear sigma model in an energy range below 10^4 in units of the mass gap $m$. We argue that the form factor approach, with the form factor series trunctated at the 6-particle level, provides an almost exact solution of the model in this energy range. The onset of the (2-loop) perturbative regime is found to occur only at energies around $100m$.Comment: 13 pages LaTex, 4 PostScript figures; version published in Physics Letters

On the Possibility of Quantum Gravity Effects at Astrophysical Scales

The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that at large distances there could be strong renormalization effects, including a scale dependence of Newton's constant, which mimic the presence of dark matter at galactic and cosmological scales.Comment: LaTeX, 18 pages, 4 figures. Invited contribution to the Int. J. Mod. Phys. D special issue on dark matter and dark energ

Quantum Einstein Gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravit

On the Ultraviolet Behaviour of Newton's constant

We clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the square of the cutoff, even though it is technically inessential. As a consequence of this behaviour, the existence of an UV Fixed Point would seem to imply that gravity has a built-in UV cutoff when described in Planck units, but not necessarily in other units.Comment: 8 pages; CQG class; minor changes and rearrangement