Related papers: Explicit Examples on Conformal Invariance

We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…

We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of space-times.

We investigate a conformal invariant gravitational model which is taken to hold at pre-inflationary era. The conformal invariance allows to make a dynamical distinction between the two unit systems (or conformal frames) usually used in…

To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a…

We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…

We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…

In this note, we illustrate how the two-dimensional theory of elasticity provides a physical example of field theory displaying scale but not conformal invariance.

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which…

QCD in $d=4-2\epsilon$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge…

We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition by revealing space-time conformal covariance of entanglement entropies and…

Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…

Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…

An effective non-local quantum field theory is constructed, which describes interaction of pomerons in the high-coloured QCD. The theory includes both splitting and merging triple pomeron vertexes and diagrams with pomeronic loops. The…

The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other…

There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in…

We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…

The emergence of conformal states is established for any problem involving a domain of scales where the long-range, SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs…