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

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

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

Europe as a Symbolic Resource - On the Discursive Space of Political Struggles in Poland

The aim of this paper is to reconstruct the structure of discursive positions pertaining to the relationship between Poland and the European Union (EU). Such a problematization draws on the assumption that Europe is always understood in relation to the nation state and, in turn, the image of the latter is explicitly referred to or can be inferred from the vision of the EU. The analysis of the empirical data has revealed three discursive positions which organize the production of meaning and govern the strategies of representation. The first position represents the EU as a chance for the further modernization of Poland. The second position perceives the EU as the game of interests between sovereign nation states. The task of the nation state is to benefit from cooperation within an extra-state structure and to retain maximum sovereignty at the same time. The third identifies the EU as a threat hostile to the nation state and its interests. The chain of equivalence connects the EU with almost all negative social phenomena. The discursive analytical assumptions adopted in the paper help to show how the same topics and words (chance, threat, interests, nation, state, sovereignty, Europe of fatherlands, and modernization) acquire different meanings in the context of particular interpretations of other words.Poland; Europeanization; Europeanization