Related papers: AdS (super)projectors in three dimensions and part…
Within the framework of ${\mathcal N}=1$ anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $\mathfrak{V}_{\alpha(m)\dot{\alpha} (n)} :=…
This thesis is dedicated to the study of (super)spin projection operators and their applications on maximally symmetric (super)space backgrounds in three and four dimensions. On such backgrounds, the irreducible representations of the…
We elaborate on the traceless and transverse spin projectors in four-dimensional de Sitter and anti-de Sitter spaces. The poles of these projectors are shown to correspond to partially massless fields. We also obtain a factorisation of the…
The N = 1 superfield formalism in four-dimensions is well formulated and understood, yet there remain unsolved problems. In this thesis, superfield actions for free massless and massive higher spin superfield theories are formulated in four…
We consider a supersymmetric extension of the algebra associated with three and four dimensional Anti de Sitter space. A representation of the supersymmetry operators in superspace is given. Supersymmetry invariant models are constructed…
Given a maximally symmetric $d$-dimensional background with isometry algebra $\mathfrak{g}$, a symmetric and traceless rank-$s$ field $\phi_{a(s)}$ satisfying the massive Klein-Gordon equation furnishes a collection of massive…
The quadratic Casimir operator of the special unitary $SU(N)$ group is used to construct projection operators, which can decompose any of its reducible finite-dimensional representation spaces contained in the tensor product of two and…
We consider unconstrained formulation of the higher spin gauge theory in anti de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin…
There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290;…
Within the framework of (2,0) anti-de Sitter (AdS) supersymmetry in three dimensions, we propose a multiplet of higher-spin currents. Making use of this supercurrent, we construct two off-shell gauge formulations for a massless multiplet of…
We classify all massive irreducible representations of super Poincar\'e in D=10. New Casimir operators of super Poincar\'e are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains…
Explicit formulae for the projectors onto invariant subspaces of the $\operatorname{ad}^{\otimes 2}$ representation of the Lie algebras $so(N)$ and $sp(2r)$ have been found by means of the split Casimir operator. These projectors have also…
We review the component Lagrangian construction of the supersymmetric higher spin models in three dimensional (3D) Minkowski and anti de Sitter (AdS) spaces. The approach is based on the frame-like gauge invariant formulation, where massive…
We derive the propagators for higher-spin master fields in anti-de Sitter space of arbitrary dimension. A method is developed to construct the propagators directly without solving any differential equations. The use of the ambient space,…
Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_L\times SU(2)_R$ that are closely related to Penrose twistors. Starting…
We study the symmetry properties of infinite spin fields in $\rm{AdS}_4$ space which are involved in the Lagrangian model proposed in arXiv:2403.14446 where the main role is played by operator constraints. It is shown that the conditions…
In three dimensions, it is known that field theories possessing extended $(p,q)$ anti-de Sitter (AdS) supersymmetry with ${\cal N}=p+q \geq 3$ can be realised in (2,0) AdS superspace. Here we present a formalism to reduce every field theory…
We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose…
We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in terms of those in d dimensional anti-de Sitter space. The procedure, which is neither dimensional reduction nor dimensional compactification, is called dimensional…
In the $N=1$ superspace, AdS$_4$ supersymmetry is realized as the non-linear super coordinate transformations. The fermionic coordinates form a faithful non-linear representation of supersymmetry on their own. By introducing an auxiliary…