Related papers: A Supertwistor Formalism for $\mathcal{N}=1,2,3,4\…
The physical states of N=4 conformal supergravity in four dimensions occur in twistor-string theory by Berkovits and Witten(hep-th/0406051). We study two alternative versions of twistor-string theory based on the B-model of weighted…
Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators…
N=1, d=4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these…
We consider a formulation of N=1 D=3,4 and 6 superparticle mechanics, which is manifestly supersymmetric on the worldline and in the target superspace. For the construction of the action we use only geometrical objects that characterize the…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
We construct a Super-Grassmannian for $n-$point functions in $\mathcal{N}=2$ to $4$ SCFT$_3$. The constraints imposed by super-conformal invariance and $R-$symmetry are completely manifest in this formalism through (operator-valued) delta…
We consider quantum supergroups that arise in non-anticommutative deformations of N=(1/2,1/2) and N=(1,1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding deformed algebras of superfields contain left…
We establish a correspondence between superembedding and supertwistor methods for constructing 4D N = 1 SCFT correlation functions by deriving a simple relation between tensors used in the two methods. Our discussion applies equally to 4D…
We study twist operators in higher dimensional CFT's. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in…
We compute the superconformal partial waves of the four-point correlator $\langle JJJJ\rangle$, in which the external operator $J$ is the superconformal primary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. We develop…
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 develop off-shell formulations for ${\cal N}=1$ and ${\cal N}=2$ anti-de Sitter supergravity theories in three spacetime dimensions that contain gauge two-forms in the auxiliary field sector. These formulations are shown to allow…
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many…
By extending the six-dimensional hybrid formalism for the superstring to include $d=6$ $\mathcal{N}=1$ superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator…
We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (\alpha_{1} \alpha_{2} \alpha_{3} \alpha_{4}) }$ which we refer to as the superspin-2 current multiplet.…
Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…
The N = 2, 4 superconformal symmetry constraints in d = 4 for four point functions of chiral primary 1/2-BPS operators are derived. The operators are described by symmetric traceless tensors of the internal R-symmetry group. A substantial…
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free…
We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…
A new type of supersymmetric twistors is proposed and they are called $\theta$-twistors versus the supertwistors. The $\theta$-twistor is a triple of spinors including the spinor superspace coordinate $\theta$ instead of the Grassmannian…