Related papers: Working with Nonassociative Geometry and Field The…
Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/ M-theory. Such nonassociative and noncommutative geometric and quantum…
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed…
We consider charged rotating BTZ black holes in noncommutative space by use of Chern-Simons theory formulation of $2+1$ dimensional gravity. The noncommutativity between the radial and the angular variables is introduced through the…
We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…
A nonabelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four spacetime dimensions. These theories involve an extended…
We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger-Simons differential characters. The space of…
We study gauge theories based on nonabelian 2-forms. Certain connections on loop space give rise to generalized covariant derivatives that include a nonabelian 2-form. This can be used to find rather straightforward expressions for the…
In this work, we show that a class of metric-affine gravities can be reduced to a Riemann-Cartan one. The reduction is based on the cancelation of the nonmetricity against the symmetric components of the spin connection. A heuristic proof,…
The transformation properties of a Kalb-Ramond field are those of a gauge potential. However, it is not clear what is the group structure to which these transformations are associated. In this paper, we complete a program started in…
We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock…
Inspired by recent studies on string theory with non-geometric fluxes, we develop a differential geometry calculus combining usual diffeomorphisms with what we call beta-diffeomorphisms. This allows us to construct a manifestly bi-invariant…
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…
We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general…
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…
We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U of M, based on the geometric and extensor calculus on an…
We develop a combinatorial theory of vector bundles with connection on locally ordered simplicial complexes. This is a first step towards a discrete exterior calculus for bundle-valued forms. The basic building block is the discrete…
The purely mathematical root of the dequantization constructions is the quest for a sheafification needed for presheaves on a noncommutative space. The moment space is constructed as a commutative space, approximating the noncommutative…
We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class…
The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form…