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Super-gauge transformations on physical space-time are defined on the projective six-dimensional hypercone. The basic observation which motivates the present approach is that the product of any two super-gauges is a general conformal (+ γ 5 ) transformation and indeed these latter transformations are simply realized on the six-dimensional hypercone. It turns out that also super-gauge transformations have a natural action on this projective space where the parameters of such transformations are (totally anticommuting) spinors which transform according to the fundamental (eight-dimensional) representation of the spinor group SU (2,2), isomorphic to the conformal group. The enlarged algebra of super-gauges, conformal and chiral transformations and its most relevant representations are discussed in the present formalism.

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced in this general framework. In particular, we extend the notions of scales, closed and exact Weyl connections, and Rho--tensors, we characterize the classes of such objects, and we use the results to give a new description of the Cartan bundles and connections for all parabolic geometries., 26 pages

In this paper we compute the holographic two-point functions of four dimensional conformal gravity. Precisely we calculate the two-point functions for Energy- Momentum (EM) and Partially Massless Response (PMR) operators that have been identified as two response functions for two independent sources in the dual CFT. The correlation function of EM with PMR tensors turns out to be zero which is expected according to the conformal symmetry. The two-point function of EM is that of a transverse and traceless tensor, and the two-point function of PMR which is a traceless operator contains two distinct parts, one for a transverse-traceless tensor operator and another one for a vector field, both of which fulfill criteria of a CFT. We also discuss about the unitarity of the theory., Comment: 42 pages. Published version in JHEP

Anisotropic fluids in general relativity that admit a conformal collineation, a generalization of a conformal motion, are considered. By investigating the kinematic properties of such fluids, and then using the field equations, some recent results on the restrictions imposed by a conformal collineation symmetry are generalized.

We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional $$ \mathcal{N}=4 $$ superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.

It is shown that conformal symmetric space‐times admitting an infinitesimal conformal symmetry are either of type O or N. Those of type N represent plane gravitational waves with parallel rays, provided the Einstein tensor is invariant of the infinitesimal conformal symmetry.

By using the dimensional regularization procedure, we explicitly calculate the coefficients of conformal anomalies in a general background metric due to scalar, spin 1 2 fermion, gauge and gravitation fields.

We introduce A Weyl integrable space-time as a consequence of a dynamical process. We study the particular case of a vector field non-minimally coupled to gravity. The consequences for cosmology are considered. We find that it is possible to connect one riemannian region of space-time with another riemannian region of space-time by a series of Weyl integrable domains.

It is argued that conformal invariance cannot in general solve the problem of renormalization in quantum gravity. This is due to the presence of conformal anomalies.

Conformal transformations are applied to the motion of a space ship experiencing a constant acceleration. The role of proper time is interpreted in terms of atomic periods, and the relationship between the conformal transformations and the general theory of relativity is clarified.

A result of W. Blaschke on conformal invariants of a surface is generalized.

Based upon the geometrical and topological method, the conformal anomaly for pure gravity in a curved space-time is discussed, and a new expression αεabcdΩabΛΩcd+βεabcdHabΛHcd of the conformal anomaly for pure gravity is obtained, where α, βare two arbitrary constants,Ωab and Hab are Riemann curvature 2-form and eonformal invariant curvature 2-form respectively introduced by Thomas. In the expression the first term is proportional to Euler class, the second term contains not only the ordinary Weyl tensor square but also the other conformal invariants.

For the first time the Hoyle-Narlikar theory with creation of matter and a variable gravitational constant G, is subjected to the following cosmological tests: (1) the magnitude versus z relation, (2) the N(m) versus m relation for quasars, (3) the metric angular diameters versus z relation, (4) the isophotal angles versus z relation, (5) the log N-log S radio source count, and finally (6) the 3 K radiation. It is shown that the theory passes all these tests just as well as the standard cosmology, with the additional advantage that the geometry of the universe is uniquely determined, with a curvature parameter equal to zero. It is also interesting to note that the variability of G affects the log N-log S curve in a way similar to the density evolution introduced in standard cosmologies. The agreement with the data is therefore achieved without recourse to an ad hoc density evolution.

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.