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We consider conformal and scale-invariant gravities in d dimensions, with a special focus on pure $R^2$ gravity in the scale-invariant case. In four dimensions, the structure of these theories is well known. However, in dimensions larger…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…
Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary we study the Weyl transformation properties of the bulk metric on shell and of the boundary action. We obtain a universal formula for one of the…
Canonical vacuum gravity is expressed in generally-covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance, the time mapping ${\T}:…
We use the Ward identities corresponding to general linear transformations, and derive relations between transport coefficients of $(2+1)$-dimensional systems. Our analysis includes relativistic and Galilean invariant systems, as well as…
We investigate the behavior of generic, matter-coupled, 2D dilaton gravity theories under dilaton-dependent Weyl rescalings of the metric. We show that physical observables associated with 2D black holes, such as the mass, the temperature…
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
Conformal algebra on R x S^3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless…
We discuss the most general class of teleparallel scalar-torsion theories of gravity in their covariant formulation. The only restrictions we impose are the invariance of the action under diffeomorphisms and local Lorentz transformations,…
The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl…
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of…
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…
Einstein gravity in the Palatini first order formalism is shown to possess a vector supersymmetry of the type encountered in the topological gauge theories. A peculiar feature of the gravitationel theory is the link of this vector…
The w_\infty algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2,3,...,\infty. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface.…
We review uniqueness results for the kinematical part of loop quantum gravity. After sketching the general loop formalism, the holonomy-flux and the Weyl algebras are introduced. In both cases, then, diffeomorphism invariant representations…
We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the…
We develop a quantum effective action for scalar-tensor theories of gravity which is both spacetime diffeomorphism invariant and field reparameterisation (frame) invariant beyond the classical approximation. We achieve this by extending the…
Two-dimensional matterless dilaton gravity is a topological theory and can be classically reduced to a (0+1)-dimensional theory with a finite number of degrees of freedom. If quantization is performed, a simple gauge invariant quantum…
We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry…