Related papers: Special geometries, from real to quaternionic
Supergravity theory in $2+\epsilon$ dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In…
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real…
We give an overview of the different non-Lorentzian supergravity theories in diverse dimensions that have been constructed in recent years. After giving a detailed discussion of non-Lorentzian geometries as compared to Lorentzian…
We construct maximal supergravity in four dimensions with local scaling symmetry as deformation of the original Cremmer-Julia theory. The different theories which include the standard gaugings are parametrized by an embedding tensor…
We study classical field theories that do not admit an action principle, implying that their formulation is entirely in terms of equations of motion. In the theories that we consider, supersymmetry is realized on the mass-shell. We will…
We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincar\'e symmetries manifestly. The remaining four supersymmetries and the rest…
The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N=1 supergravity in four dimensions (4D). This formalism is universal,…
These lectures are intended as a broad introduction to Chern Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant action -in the sense of fiber bundles- in more than three…
This is a light and short review on the geometry of hypermultiplets coupled to supergravity and its appearance in string theory. As is long known, the target space of the hypermultiplet sigma-model is a quaternion-K\"ahler (QK) manifold of…
I will report on a top-down approach relating N=2, D=4 pure supergravity with non-trivial boundary behavior to a (2+1)-dimensional analog model which is able to describe the electronic properties of graphene-like materials. This is…
The target space geometry of abelian vector multiplets in ${\cal N}= 2$ theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce…
A large class of supergravities in diverse dimensions are surveyed. This includes maximal supergravities, their general gaugings in the framework of embedding tensor formalism, supergravities with less than maximal supersymmetry, their…
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as…
We analyze two models of random geometries~: planar hyper-cubic random surfaces and four dimensional simplicial quantum gravity. We show for the hyper-cubic random surface model that a geometrical constraint does not change the critical…
We give a gentle introduction to the global geometric formulation of the bosonic sector of four-dimensional supergravity on an oriented four-manifold $M$ of arbitrary topology, providing a geometric characterization of its U-duality group.…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry of Lorentz, Einstein and Minkowski comes from a projective…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is…
We present a pedagogical discussion of the emergence of gauged supergravities from M-theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional…