Quantization of the particle with a linear massless solution

In this work, a solution linear in the momentum for the massless constraint $P^{m}P_{m}=0$ is investigated. It is presented in terms of a $SO(2n,\mathbb{C})$ to $U(n)$ decomposition and interpreted in terms of projective pure spinors, which are known to parametrize the $\tfrac{SO(2n)}{U(n)}$ coset. The worldline action is quantized using the BRST formalism and, using the results of Berkovits and Cherkis, the ghost number zero wave function is shown to generate massless solutions for field equations of arbitrary spin. The model can be covariantly expressed by the action recently proposed in $D=10$ by Berkovits, in terms of a twistor-like constraint. However, a thorough account of its gauge symmetries does not lead to a spacetime supersymmetric theory. In order to derive from first principles the superparticle in the pure spinor formalism, a new model is proposed with partial worldline supersymmetry. The gauge algebra is then analyzed within the Batalin-Vilkovisky formalism and the gauge fixed action is finally shown to describe the pure spinor superparticle times a $U(1)$ decoupled sector.Comment: 20 pages. Small clarification added to the published versio

Spectrum generating algebra for the pure spinor superstring

In this work, a DDF-like construction within the pure spinor formalism is presented. Starting with the light-cone massless vertices, the creation/annihilation algebra is derived in a simple manner, enabling a systematic construction of the physical vertex operators at any mass level in terms of $SO\left(8\right)$ superfields, in both integrated and unintegrated forms.Comment: 10 pages. Added comments and reference to the paper of Mukhopadhyay. Published versio

Notes on the pure spinor b ghost

In this work, a particular BRST-exact class of deformations of the b ghost in the non-minimal pure spinor formalism is investigated and the impact of this construction in the $\mathcal{N}=2$ $\hat{c}=3$ topological string algebra is analysed. As an example, a subclass of deformations is explicitly shown, where the U(1) current appears in a conventional form, involving only the ghost number currents. Furthermore, a c ghost like composite field is introduced, but with an unusual construction.Comment: 19 pages; footnotes added; typos fixed; Published versio

On the field-antifield (a)symmetry of the pure spinor superstring

In this work, the DDF-like approach to the pure spinor cohomology is extended to the next ghost number level, the so called antifields. In a direct (supersymmetric) parallel to the bosonic string, some properties of the ghost number two cohomology are derived with the enlargement of the DDF algebra. Also, the DDF conjugates of the b ghost zero mode emerge naturally from the extended algebra and the physical state condition is discussed. Unlike the bosonic string case, the cohomology analysis of the pure spinor b ghost is restricted to BRST-closed states.Comment: 54 pages (including review section and two appendices). Comments added in the Introduction. Published versio

Light-Cone Analysis of the Pure Spinor Formalism for the Superstring

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2\pi i}\oint\lambda^{\alpha}d_{\alpha}$. In this paper, a similarity transformation is found which simplifies the form of $Q$ and maps the light-cone description of the superstring vertices into DDF-like operators in the cohomology of $Q$.Comment: 16 pages. Added reference to the paper of Mukhopadhya