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A class of 2-dimensional models including 2-d dilaton gravity, spherically symmetric reduction of d-dimensional Einstein gravity and other related theories are classically analyzed. The general analytic solutions in the absence of matter…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We…
We present the BRST formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge-fixing for the…
In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic…
Two-dimensional scalar field theories with spontaneous symmetry breaking subject to the action of Jackiw-Teitelboim gravity are studied. Solutions for the $\phi^4$ and sine-Gordon self-gravitating kinks are presented, both for general…
A class of explicitly integrable models of 1+1 dimensional dilaton gravity coupled to scalar fields is described in some detail. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and…
We construct all possible Weyl invariant actions in $d=4$ for linearized spin three field in a general gravitational background. The first action is obtained as the square of the generalized Weyl tensor for a spin three gauge field in…
We briefly outline several main results concerning various new physically relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$ gravity in the first-order formalism, coupled to a special kind of nonlinear…
The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity. We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity including…
String theory is arguably the best candidate for a theory of quantum gravity and unified interactions. Reconciling Einstein's theory of General Relativity with Quantum Mechanics. The theory however is best understood on Minkowski and…
A new class of two dimensional integrable field theories, based on the mathematical notion of Poisson manifolds, and containing gravity-Yang-Mills systems as well as the G/G gauged Wess-Zumino Witten-model, are presented. The local…
We survey a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. This theory is being currently developed jointly with K. Wysocki and E. Zehnder. The basic feature of these new spaces is that in…
In dimensions larger than 3 a modified field strength for Rarita-Schwinger type fields is constructed whose components are not constrained by the field equations. In supergravity theories the result provides a modified (supercovariant)…
The complexified gauging of the de Sitter group gives a unified theory for the electroweak and gravitational interactions. The standard spectrum for the electroweak gauge bosons is recovered with the correct mass assignments, following a…
We consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner-Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function…
A massless spinor field is quantized in the background of a singular static magnetic vortex in 2+1-dimensional space-time. The method of self-adjoint extensions is employed to define the most general set of physically acceptable boundary…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's…
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the…