Related papers: The tensor hierarchy simplified
We argue that the gauge $SL(2N,C)$ theories may point to a possible way where the known elementary forces, including gravity, could be consistently unified. Remarkably, while all related gauge fields are presented in the same adjoint…
IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and…
A recollection of some theoretical developments that preceded and followed the first formulation of supergravity theory is presented. Special emphasis is placed on the impact of supergravity on the search for a unified theory of fundamental…
In the low-energy limit, M-theory compactified on S1/Z2 is formulated in terms of Bianchi identities with sources localized at orbifold singularities and anomaly-cancelling counterterms to the Wilson effective Lagrangian. Compactifying to…
A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
In an ungauged supergravity theory, the presence of a \emph{scalar potential} is allowed only for the minimal $\N=1$ case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking…
We reconsider the well-known issue of string corrections to Supergravity theory. Our treatment is carried out to second order in the string slope parameter. We establish a procedure for solving the Bianchi identities in the non minimal…
The perspective that gravity may govern the unification of all elementary forces calls for extending the gauge-gravity symmetry $SL(2,C)$ to the broader local symmetry $SL(2N,C)$, where $N$ reflects the internal $SU(N)$ subgroup. This…
Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we…
A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the…
We present a formulation of gravity in terms of a theory based on complex SU(2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-self-duality of the field strength…
Magical supergravities are a very special class of supergravity theories whose symmetries and matter content in various dimensions correspond to symmetries and underlying algebraic structures of the remarkable geometries of the Magic Square…
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
Describing the gravitational energy and momentum, the Bel-Robinson tensor is the best tensor. However, the classical pseudotensors can also manage the the same job. As Deser mentioned in 1999, a certain linear combination between Einstein…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…
The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant…
In the continuum the Bianchi identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi…
We obtain a bosonization prescription that allows to represent the energy-momentum tensor and supersymmetry generators of non-critical superstring theories with minimal matter as those of topological supergravity. Superstrings with $N=1$…