Related papers: Noncommutative Gravity in Six Dimensions
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The model in this regime is solvable and the corresponding exact beta function is…
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…
In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study…
Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the…
A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index ${\cal P}_{2n}$ plays a crucial role in both gravity and gauge theories. ${\cal P}_{2n}(gravity)$ gives the gravitational…
There are strong restrictions on the possible representations and in general on the matter content of gauge theories formulated on noncommutative Moyal spaces, termed as noncommutative gauge theory no-go theorem. According to the no-go…
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of $W_\infty$-gravity is analysed in detail. While…
It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of…
Based on the observation that the dimension of the tangent space is not necessarily equal to the dimension of the corresponding curved manifold and on the known fact that gravitational theories can be formulated in a gauge theoretic way, we…
In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the…
We consider a $SO(d)$ gauge theory in an Euclidean $d$-dimensional space-time, which is known to be renormalizable to all orders in perturbation theory for $2\le{d}\le4$. Then, with the help of a space-time representation of the gauge…
We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of $SO(12),$ we show that the quantum field theory…
An N=1/2 supergravity in four Euclidean spacetime dimensions, coupled to both vector- and scalar-multiplet matter, is constructed for the first time. We begin with the standard (1,1) conformally extended supergravity in four Euclidean…
We investigate the weak gravity bounds on the U(1) gauge theory and scalar field theories in various dimensional noncommutative space. Many results are obtained, such as the upper bound on the noncommutative scale $g_{YM}M_p$ for four…
We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…