Related papers: Conformal invariance versus Weyl invariance
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyl- and conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is…
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that…
Flat-space conformal invariance and curved-space Weyl invariance are simply related in dimensions greater than two. In two dimensions the Liouville theory presents an exceptional situation, which we here examine.
While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field theories with discrete dilatation spectrum, it is not the case in more general…
In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.
The present work deals with two different but subtilely related kinds of conformal mappings: Weyl rescaling in $d>2$ dimensional spaces and SO(2,d) transformations. We express how the difference between the two can be compensated by…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action.…
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…
Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -- represented by an action principle and the derived motion…
For a four dimensional, unitary, diffeomorphism- and scale invariant quantum field theory without higher derivatives and a well defined scale current we argue that scale invariance implies conformal invariance. The proof relies on the…
Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
In a previous paper conformal gravity was derived by means of a precise action principle on the hypercone in the conformal space. Here it is shown that the same technique used to construct conformal spin two theory as represented by linear…
We show that there exist conformally invariant theories for all spins in d=4 de Sitter space, namely the partially massless models with higher derivative gauge invariance under a scalar gauge parameter. This extends the catalog from the two…
Using an approach based on the Casimir operators of the de Sitter group, the conformal invariant equations for a fundamental spin-2 field are obtained, and their consistency discussed. It is shown that, only when the spin-2 field is…
Conventional quantization of two-dimensional diffeomorphism and Weyl invariant theories sacrifices the latter symmetry to anomalies, while maintaining the former. When alternatively Weyl invariance is preserved by abandoning diffeomorphism…