Related papers: U-gravity : ${\mathbf{SL}(N)}$
This is the first part of an investigation concerning the formulation of 2D gravity in the framework of the uniformization theory of Riemann surfaces. As a first step in this direction we show that the classical Liouville action appears in…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
A system of gravity coupled to a 2-form gauge field, a dilaton and Yang-Mills fields in $2n$ dimensions arises from the (2,1) sigma model or string. The field equations imply that the curvature with torsion and Yang-Mills field strength are…
It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a…
We show that it is possible to formulate gravity with a complex vierbein based on SL(2,C) gauge invariance. The proposed action is a four-form where the metric is not introduced but results as a function of the complex vierbein. This…
We construct the 12-dimensional exceptional field theory associated to the group $\mathrm{SL}(2) \times \mathbb{R}^+$ . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that…
Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory.…
In a preceding paper we developed a reformulation of Newtonian gravitation as a {\it gauge} theory of the extended Galilei group. In the present one we derive two true generalizations of Newton's theory (a {\it ten-fields} and an {\it…
A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular…
We conjecture that $W$ gravity can be interpreted as the gauge theory of $\phi$ diffeomorphisms in the space of dimensionally-reduced $D=2+2$ $SU^*(\infty)$ Yang-Mills instantons. These $\phi$ diffeomorphisms preserve a volume-three form…
The aim of this Thesis is twofold. On the one hand, we find the necessary and sufficient conditions for a maximally supersymmetric supergravity theory in 3D to be a solution of 11D supergravity (but the result is general and also holds for…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
After reviewing briefly the classical examples of duality in four dimensional field theory we present a generalisation to arbitrary dimensions and to p-form fields. Then we explain how U-duality may become part of a larger non abelian…
Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
Einstein Gravity can be formulated as a gauge theory with the tangent space respecting the Lorentz symmetry. In this paper we show that the dimension of the tangent space can be larger than the dimension of the manifold and by requiring the…
We show that gravity together with curved spacetime can emerge, at the microscopic scale, from a U(1) gauge field. The gauge boson that carries gravity, of elementary particles, is proved to be a spin one massless and electrically neutral…
The N=1 self-dual supergravity has SL(2,C) and the left-handed and right -handed local supersymmetries. These symmetries result in SU(2) charges as the angular-momentum and the supercharges. The model possesses also the invariance under the…
U-duality imposes strong constraints on the structure of divergences in supergravity. But Gaillard-Zumino Sp$(2n_v, \mathbb{R})$ duality in D=4 has more symmetries than U-duality. For example, in $N = 8$ the dimension of Sp(56) is 1596,…