Related papers: Finite Gauge Transformations and Geometry in Doubl…
We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for the frame-like and…
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also…
We revisit the generalized connection of Double Field Theory. We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity…
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized…
Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…
We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying…
We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation…
We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their…
It is possible to characterize certain states of matter by properties of their edge states. This implies a notion of `surface-only models': models which can only be regularized at the edge of a higher-dimensional system. After incorporating…
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations…
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case…
We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…