Supersymmetry and superspace: Introduction: from R^Tp/q to supersymmetry Superalgebras, Grassmann-shells and super Lie groups The Poincar^D'e superalgebra Unitary representation of the Poincar^D'e superalgebra Real superspace R^T4/4 and superfields Complex superspace C^T4/2, chiral superfields and covariant derivatives The on-shell massive superfield representations The on-shell massless superfield representations From superfields to component fields The superconformal group. Mathematical background: The Poincar^D'e group, the Lorentz group Finite-dimensional representations of ^ISpin(3,1) The Lorentz algebra Two-component and four-component spinors Representations of the Poincar^D'e group Elements of differential geometry and gravity The conformal group The mass-shell field representation Elements of algebra with supernumbers Elements of analysis with supernumbers The supergroup of general coordinate transformations on R^Tp/q. However, there is a natural interpretation of this fact recently proposed, whereby our spacetime can be viewed as a subsystem. In a naive interpretation, the presence of a second connection field with identical quantum numbers as the 'physical' connection might seem embarrassing. Transgressions are invariant functions that depend on two independent connection field, that interact at the boundary of spacetime. Transgression forms are mathematical objects that play an important role in the Chern–Weil theorems in algebraic topology. This modification turn the lagrangian into a transgression. The need to regularize these theories in order to define conserved charges and thermodynamic functions in asymptotically AdS spacetimes, requires the addition of a very special boundary terms to the action. The supersymmetric extensions of these theories exist for the AdS and Poincaré groups, and the fields are components of a single connection for the corresponding Lie algebras. Simons family and are particular cases of the so-called Lovelock gravities, constructed as the dimensional continuations of the lower dimensional Euler classes. We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincaré transformations can be constructed in all odd dimensions. The construction of the associated centrally extended surface charge algebra. The derivation of how this symmetry algebra is realized on solution space and The firstĪpplications are studied: an exact representation by bulk vector fields of theĪsymptotic symmetry algebra through the introduction of a modified Lie bracket, Transformations and not, as usually done, with the Lorentz algebra. In particular, it is argued that the symmetry algebra ofĪsymptotically flat spacetimes at null infinity in 4 dimensions should be takenĪs the semi-direct sum of supertranslations with infinitesimal local conformal Symmetries and classical solutions involved in the AdS3/CFT2 correspondence, weĪpply a similar analysis to asymptotically flat spacetimes at null infinity inģ and 4 dimensions. The second part is devoted to the study ofĪsymptotic symmetries and their applications to holography. The role of the second hamiltonian is played by theĮlectromagnetic duality generator. Reduced phase-space, all higher spin gauge fields can be written asīi-hamiltonian systems. Write an action manifestly invariant under duality rotations in presence ofīoth electric and magnetic external sources. An extendedĭouble potential formalism for linearized gravity is introduced which allows to Some properties of the electromagnetic duality in 4 dimensions. We also demonstrate that the gauge symmetries present in the formulation are all Stueckelberg-like so that the continuous spin system is not a genuine gauge theory. We show that the naive choice leads to an empty system and propose a suitable class resulting in the correct degrees of freedom.

Because a continuous spin system inevitably involves infinite number of fields, specification of the allowed class of field configurations becomes a part of its definition. In particular, for scalar continuous spin fields we reproduce the Bekaert-Mourad formulation and the Schuster-Toro formulation. The description is shown to produce generalized versions of triplet, metric-like, and light-cone formulations. It is based on the appropriately modified version of the constrained system originally used to describe massless bosonic fields of mixed-symmetry type. We propose a description of continuous spin massless fields of mixed-symmetry type in Minkowski space at the level of equations of motion.

Sso 2016 ghost in forgotten fields