Lower-dimensional pure-spinor superstrings

We study to what extent it is possible to generalise Berkovits' pure-spinor construction in d=10 to lower dimensions. Using a suitable definition of a ``pure'' spinor in d=4,6, we propose models analogous to the d=10 pure-spinor superstring in these dimensions. Similar models in d=2,3 are also briefly discussed.Comment: 17 page

An Introduction to the Covariant Quantization of Superstrings

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.Comment: LaTex, 23 pp. Contribution to the Proceedings of the Workshop in String Theory, Leuven 2002, some references added and a comment on ref. [16

The Algebraic Method

Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process $b\to s\gamma$.Comment: Latex, 38 page

BFT embedding of the Green-Schwarz superstring and the pure spinor formalism

We worked out the Batalin-Fradkin-Tyutin (BFT) conversion program of second class constraints to first class constraints in the GS superstring using light cone coordinates. By applying this systematic procedure we were able to obtain a gauge system that is equivalent to the recent model proposed by Berkovits and Marchioro to relate the GS superstring to the pure spinor formalism.Comment: 12 pages latex2e, v2 typos fixed, v3 published in JHE

Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation

In order to gain deeper understanding of pure-spinor-based formalisms of superstring, an explicit similarity transformation is constructed which provides operator mapping between the light-cone Green-Schwarz (LCGS) formalism and the extended pure spinor (EPS) formalism, a recently proposed generalization of the Berkovits' formalism in an enlarged space. By applying a systematic procedure developed in our previous work, we first construct an analogous mapping in the bosonic string relating the BRST and the light-cone formulations. This provides sufficient insights and allows us to construct the desired mapping in the more intricate case of superstring as well. The success of the construction owes much to the enlarged field space where pure spinor constraints are removed and to the existence of the ``B-ghost'' in the EPS formalism.Comment: 37pages, no figur

Minimal D=7D=7 Supergravity and the supersymmetry of Arnold-Beltrami Flux branes

In this paper we study some properties of the newly found Arnold-Beltrami flux-brane solutions to the minimal $D=7$ supergravity. To this end we first single out the appropriate Free Differential Algebra containing both a gauge $3$-form $\mathbf{B}^{[3]}$ and a gauge $2$-form $\mathbf{B}^{[2]}$: then we present the complete rheonomic parametrization of all the generalized curvatures. This allows us to identify two-brane configurations with Arnold-Beltrami fluxes in the transverse space with exact solutions of supergravity and to analyze the Killing spinor equation in their background. We find that there is no preserved supersymmetry if there are no additional translational Killing vectors. Guided by this principle we explicitly construct Arnold-Beltrami flux two-branes that preserve $0$, $1/8$ and $1/4$ of the original supersymmetry. Two-branes without fluxes are instead BPS states and preserve $1/2$ supersymmetry. For each two-brane solution we carefully study its discrete symmetry that is always given by some appropriate crystallographic group $\Gamma$. Such symmetry groups $\Gamma$ are transmitted to the $D=3$ gauge theories on the brane world--volume that occur in the gauge/gravity correspondence. Furthermore we illustrate the intriguing relation between gauge fluxes in two-brane solutions and hyperinstantons in $D=4$ topological sigma-models.Comment: 56 pages, LaTeX source, 8 jpg figures, typos correcte

Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds

We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.Comment: 31 pp. no figures, latex, some modifications at pag 21, a missing term in 4.51 corrected. Discussion on BRST symmetry improve

Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --

In a previous work, we have constructed a reparametrization invariant worldsheet action from which one can derive the super-Poincare covariant pure spinor formalism for the superstring at the fully quantum level. The main idea was the doubling of the spinor degrees of freedom in the Green-Schwarz formulation together with the introduction of a new compensating local fermionic symmetry. In this paper, we extend this "double spinor" formalism to the case of the supermembrane in 11 dimensions at the classical level. The basic scheme works in parallel with the string case and we are able to construct the closed algebra of first class constraints which governs the entire dynamics of the system. A notable difference from the string case is that this algebra is first order reducible and the associated BRST operator must be constructed accordingly. The remaining problems which need to be solved for the quantization will also be discussed.Comment: 40 pages, no figure, uses wick.sty; v2: a reference added, published versio