Related papers: Explaining the Pure Spinor Formalism for the Super…
These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts…
The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First we prove that the pure spinor formula to compute SYM tree amplitudes derived in…
We discuss string spectra in the low-tension limit using the BRST formalism, with emphasis on the role of triplets of totally symmetric tensors and spinor-tensors and their generalizations to cases with mixed symmetry and to (A)dS…
We compute partition functions describing multiplicities and charges of massless and first massive string states of pure-spinor superstrings in 3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet of minimal…
The 1.5 order formalism (sometimes called a `trick') is the cornerstone of modern supergravity. In this paper, the free massive Wess--Zumino theory is used as a simple toy model to look at the BRS symmetry of the first, second and 1.5 order…
In this note, we study, formalize, and generalize the pure spinor superfield formalism from a rather nontraditional perspective. To set the stage, we review the notion of a multiplet for a general super Lie algebra, working in the context…
The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer $W_{2,s}$ strings, where the BRST charge is written as $Q_B=Q_0+Q_1$. Using this method, we reconstruct the nilpotent BRST charges $Q_{0}$ for the…
We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even…
We present a novel ten-dimensional description of ambitwistor strings. This formulation is based on a set of supertwistor variables involving pure spinors and a set of constraints previously introduced in the context of the $D=10$…
We investigate the spin-statistics connection in arbitrary dimensions for hermitian spinor or tensor quantum fields with a rotationally invariant bilinear Lagrangian density. We use essentially the same simple method as for space dimension…
The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a…
I review the covariant quantization of the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. The BRST analysis yields massless bosonic and fermionic vertex operators in various ghost and picture number sectors,…
The physical states of D=5 holomorphic Chern-Simons theory correspond to on-shell D=10 open superstring states in the cohomology of $q_+$, where $q_+$ is one of the 16 spacetime supersymmetry generators. Scattering amplitudes of these…
We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…
In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we…
The twenty-one-vertex model, the spin $1$ analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the $2\times 2$-fold fusion SOS model and vertex-face transformation. The tail…
The so-called Lounesto's classification engenders six distinct classes of spinors, divided into two sectors: one composed by regular spinors (single-helicity spinors) and the other composed by singular spinors (comprising dual-helicity…
We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of…
We consider the BRST and superconformal properties of the ghost action of 2-D supergravity. Using the background spin structure on the worldsheet, we show that this action can be transformed by canonical field transformations to reach other…
BRST operators for two-dimensional theories with spin-2 and spin-$s$ currents, generalising the $W_3$ BRST operator of Thierry-Mieg, have previously been obtained. The construction was based on demanding nilpotence of the BRST operators,…