相关论文: Scale without Conformal Invariance: Theoretical Fo…

With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a…

We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a…

Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be…

Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…

We examine the question of scale vs. conformal invariance for the linearized Einstein-Hilbert action, which describes the IR fixed point of quantum gravity. In $D = 4$, although the action is not conformally invariant in the usual sense, we…

We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's…

The gradient property of the renormalisation group (RG) is examined to four-loop order in scalar-fermion systems in $d=4$ and $d=4-\varepsilon$ dimensions. The crucial role played by the beta shift, which is a modification of the standard…

We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not…

When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this…

We study scale invariance at the quantum level (three loops) in a perturbative approach. For a scale-invariant classical theory the scalar potential is computed at three-loop level while keeping manifest this symmetry. Spontaneous scale…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories, scale…

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…

In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the…

We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant…

Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…

We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the $U(1)$ particle number or the Galilean…

The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…

We consider a model for gravity that is invariant under global scale transformations. It includes one extra real scalar field coupled non-minimally to the gravity fields. In this model all the dimensionful parameters like the gravitational…