Functional and Local Renormalization Groups

We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example. We show that away from criticality the Wess-Zumino action is described by a derivative expansion with coefficients naturally related to RG quantities. We then demonstrate that the Weyl consistency conditions derived in the LRG approach are equivalent to the RG equation for the $c$-function available in the FRG scheme. This allows us to give an explicit FRG representation of the Zamolodchikov-Osborn metric, which in principle can be used for computations.Comment: 19 pages, 1 figur

Asymptotic freedom in Horava-Lifshitz gravity

We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.Comment: 4 pages, 2 figure

Applications of the Functional Renormalization Group: From Statistical Models to Quantum Gravity

The present dissertation is essentially a collection of three investigations, in the context of the functional Renormalization Group. First, we will apply it to scalar models with internal O(N) symmetry, to study their universality classes and how the Mermin-Wagner theorem is seen in the RG framework. Next, we will use it to study Weyl-invariant systems, and in particular to obtain a nonperturbative proof that a quantization procedure respecting Weyl invariance is always possible, regardless of the field content of the theory. Finally, to investigate the corrections to the gravitational beta functions due to the anomalous dimensions of gravitons and ghosts

A functional RG equation for the c-function

After showing how to prove the integrated c-theorem within the functional RG framework based on the effective average action, we derive an exact RG flow equation for Zamolodchikov's c-function in two dimensions by relating it to the flow of the effective average action. In order to obtain a non-trivial flow for the c-function, we will need to understand the general form of the effective average action away from criticality, where nonlocal invariants, with beta functions as coefficients, must be included in the ansatz to be consistent. We then apply our construction to several examples: exact results, local potential approximation and loop expansion. In each case we construct the relative approximate c-function and find it to be consistent with Zamolodchikov's c-theorem. Finally, we present a relation between the c-function and the (matter induced) beta function of Newton's constant, allowing us to use heat kernel techniques to compute the RG running of the c-function.Comment: 41 pages, 17 figures; v2: some minor correction

Quantum Gravity signatures in the Unruh effect

We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the "Unruh dimension" as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.Comment: 38 pages, 7 figures; v3: section 2 rewritten, references adde

Scaling and Renormalization in two dimensional Quantum Gravity

We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal dimension of the theory and the scaling of the reparametrization-invariant two point function. Then we compute the scaling exponents entering in this relations by means of the functional RG. We show that a key ingredient to obtain the correct results already known from Liouville theory is the use of the exponential parametrization for metric fluctuations. We also show that with this parametrization we can recover the correct finite part of the effective action as the $\epsilon \to 0$ continuation of gravity in $d=2+\epsilon$ dimensions.Comment: 39 page

Crossing alone the Mediterranean sea. Some critical issues about unaccompanied minors in Europe

Abstract Despite the increasing social impact of unaccompanied migrant minors (UAMs) in many European Union (EU) member states, EU regulations on UAMs are still inadequate and the necessary protection measures are thus insufficient. More specifically, the "best interest of the child", stated in a large number of international documents, may not be properly guaranteed. In addition, there is often a discrepancy between the rights of migrant children, according to the international legislation, and the actual protection they receive. Moreover, despite the declared aim of reaching a common standard of reception and inclusion, policies and practices across Europe are still very different. The paper attempts to highlight and discuss some critical issues regarding UAMs in Europe. Over and beyond the need for the EU to develop a common framework, greater efforts should be made in order to improve inclusion of UAMs, especially to ensure the management of the phenomenon beyond the current emergency