Related papers: An action principle for the Einstein-Weyl equation…
A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an…
We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency…
Metric-affine geometry provides a non-trivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the space-time (with non-vanishing torsion and…
We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…
In this paper, two things are done. (i) Using cohomological techniques, we explore the consistent deformations of linearized conformal gravity in 4 dimensions. We show that the only possibility involving no more than 4 derivatives of the…
Einstein-Weyl geometry is a triple (D,g,w), where D is a symmetric connection, [g] is a conformal structure and w is a covector such that: (i) connection D preserves the conformal class [g], that is, Dg=wg; (ii) trace-free part of the…
In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsionless but not metric-compatible, the non-metricity tensor being determined by a vector…
We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl conformal geometry in $d$ dimensions and obtain a general theory of gravity with Weyl gauge symmetry of dilatations (Weyl-DBI). This is done in the Weyl gauge covariant…
We consider $f(R)$ gravity and Born-Infeld-Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the…
Weyl derivatives, Weyl-Lie derivatives and conformal submersions are defined, then used to generalize the Jones-Tod correspondence between selfdual 4-manifolds with symmetry and Einstein-Weyl 3-manifolds with an abelian monopole. In this…
In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of a spacetime symmetry, the Weyl gauge theory (of dilatations and Poincar\'e symmetry). The initial physical…
The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent…
This paper presents the detailed, standard treatment of a simple, gauge invariant action for Weyl and Weyl-like Cartan geometries outlined in a previous paper. In addition to the familiar scalar curvature squared and Maxwell terms, the…
We consider four (real or complex) dimensional hyper-K\"ahler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for…
A unitary gravitational action up to third order of curvature in which respects to the holographic $a-$theorem has been constructed in \cite{myers}. In particular, its third order term is just the Weyl-cubed term in four dimensions. In this…
We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance…
Recently, it has been pointed out that dimensionless actions in four dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed {\it restricted Weyl…
We study Weyl conformal geometry as a general gauge theory of the Weyl group (of Poincar\'e and dilatations symmetries) in a manifestly Weyl gauge covariant formalism in which this geometry is automatically metric and physically relevant.…
We comment on some peculiarities of matter with and without Weyl invariance coupled to classical $2d$ Einstein-Hilbert gravity for several models, in particular, related to the counting of degrees of freedom and on the dynamics. We find…
We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model…