Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring

Although it is not known how to covariantly quantize the Green-Schwarz (GS) superstring, there exists a semi-light-cone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi-light-cone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring.Comment: 16 pages, JHEP format, fixed typos and added 2 footnote

D=11 supergravity with manifest supersymmetry

The complete supersymmetric action for eleven-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.Comment: 14 pp., plain te

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

A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring

Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge $Q$ of the conventional PS formalism is promoted to a bona fide nilpotent charge $\hat{Q}$, the cohomology of which is equivalent to the constrained cohomology of $Q$. This construction requires only a minimum number (five) of additional fermionic ghost-antighost pairs and the vertex operators for the massless modes of open string are obtained in a systematic way. Furthermore, we present a simple composite "$b$-ghost" field $B(z)$ which realizes the important relation $T(z) = \{\hat{Q}, B(z)\}$, with $T(z)$ the Virasoro operator, and apply it to facilitate the construction of the integrated vertex. The present formalism utilizes U(5) parametrization and the manifest Lorentz covariance is yet to be achieved.Comment: 38 pages, no figure. Proof of triviality of delta-homology improved and a reference adde

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

A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism

Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.Comment: 56 pages, typos correcte

Explaining the Pure Spinor Formalism for the Superstring

After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b,c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.Comment: Added two footnotes and references to Baulieu et a

Origin of Pure Spinor Superstring

The pure spinor formalism for the superstring, initiated by N. Berkovits, is derived at the fully quantum level starting from a fundamental reparametrization invariant and super-Poincare invariant worldsheet action. It is a simple extension of the Green-Schwarz action with doubled spinor degrees of freedom with a compensating local supersymmetry on top of the conventional kappa-symmetry. Equivalence to the Green-Schwarz formalism is manifest from the outset. The use of free fields in the pure spinor formalism is justified from the first principle. The basic idea works also for the superparticle in 11 dimensions.Comment: 21 pages, no figure; v2: refs. adde

Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5 Background

We will discuss some properties of the pure spinor string on the AdS_5 x S_5 background. Using the classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around AdS_5 x S_5 background.Comment: 26. pages, added references, v2:corrected typo