Massive Superstring Vertex Operator in D=10 Superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincar\'e covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.Comment: Added reference

Covariant Matrix Model of Superparticle in the Pure Spinor Formalism

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under $SO(1,10)$ Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.Comment: 13 pages, no figures, two references adde

Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism

Although the AdS_5xS^5 worldsheet action is not quadratic, some features of the pure spinor formalism are simpler in an AdS_5xS^5 background than in a flat background. The BRST operator acts geometrically, the left and right-moving pure spinor ghosts can be treated as complex conjugates, the zero mode measure factor is trivial, and the b ghost does not require non-minimal fields. Furthermore, a topological version of the AdS_5xS^5 action with the same worldsheet variables and BRST operator can be constructed by gauge-fixing a G/G principal chiral model where G=PSU(2,2|4). This topological model is argued to describe the zero radius limit that is dual to free N=4 super-Yang-Mills and can also be interpreted as an "unbroken phase" of superstring theory.Comment: 39 pages harvma

A Note on the Classical BRST Symmetry of the Pure Spinor String in a Curved Background

The classical pure spinor version of the heterotic superstring in a supergravity and super Yang-Mills background is considered. We obtain the BRST transformations of the world-sheet fields. They are consistent with the constraints obtained from the nilpotence of the BSRT charge and the holomorphicity of the BRST current.Comment: References adde

Pure Spinor Formalism as an N=2 Topological String

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted $\hat c$=3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.Comment: 34 pages harvmac te

Pure spinors, twistors, and emergent supersymmetry

Starting with a classical action whose matter variables are a d=10 spacetime vector $x^m$ and a pure spinor $\lambda^\alpha$, the pure spinor formalism for the superstring is obtained by gauge-fixing the twistor-like constraint $\partial x^m (\gamma_m \lambda)_\alpha =0$. The fermionic variables $\theta^\alpha$ are Faddeev-Popov ghosts coming from this gauge-fixing and replace the usual (b,c) ghosts coming from gauge-fixing the Virasoro constraint. After twisting the ghost-number such that $\theta^\alpha$ has ghost-number zero and $\lambda^\alpha$ has ghost-number one, the BRST cohomology describes the usual spacetime supersymmetric states of the superstring.Comment: 10 pages harvmac tex, added comments on small Hilbert space and U_0 dependenc

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

Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.Comment: 10 pages, harvmac TeX. v2: Updated affiliation and Report-no

BRST Anomaly and Superspace Constraints of the Pure Spinor Heterotic String in a Curved Background

The pure spinor heterotic string in a generic super Yang-Mills and supergravity background is considered. We determine the one-loop BRST anomaly at the cohomological level. We prove that it can be absorbed by consistent corrections of the classical constraints due to Berkovits and Howe, in agreement with the Green-Schwarz cancelation mechanism.Comment: harvmac-big, 18 pages; references added; minor correction

One Loop Conformal Invariance of the Superstring in an AdS_5 x S^5 Background

It is proven that the pure spinor superstring in an AdS_5 x S^5 background remains conformally invariant at one loop level in the sigma model perturbation theory.Comment: 14 pages harvma