Related papers: Scale without Conformal Invariance: Theoretical Fo…
We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…
By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory.…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely…
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this…
We study global scale invariance along with the unimodular gravity in the vacuum. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar…
There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In…
We show that scale invariance provides a solution to the fine tuning problem of the cosmological constant. We construct a generalization of the standard model of particle physics which displays exact quantum scale invariance. The matter…
Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In…
A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of non-perturbative flow equations governing the evolution of the new…
The field theoretic renormalization group (RG) is applied to the problem of a passive scalar advected by the Gaussian self-similar velocity field with finite correlation time and in the presence of an imposed linear mean gradient. The…
The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a…
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and…
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of…
Scale without conformal symmetry corresponds to an inhomogeneous conservation equation for the virial current sourced by the trace of the energy-momentum tensor. Fluids that are just scale-invariant differ qualitatively from their conformal…
We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. Motivated by shell model observations, we develop a similarity theory for the inertial…
Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics…
A genuine dilaton $\sigma$ allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP) $\alpha_{\text{IR}}$ through dimensional transmutation. These large…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We…