First Massive State of the Superstring in Superspace

Using the manifestly spacetime supersymmetric description of the four-dimensional open superstring, we construct the vertex operator in superspace for the first massive state. This construction provides an N=1 D=4 superspace representation of the massive spin-2 multiplet.Comment: 7 pages late

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

Supersymmetric Born-Infeld from the Pure Spinor Formalism of the Open Superstring

Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N=1 D=10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions.Comment: Added footnote 3 in agreement with the comments of Schiappa and Wyllard in hep-th/050312

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

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

Regularizing Cubic Open Neveu-Schwarz String Field Theory

After introducing non-minimal variables, the midpoint insertion of Y\bar Y in cubic open Neveu-Schwarz string field theory can be replaced with an operator N_\rho depending on a constant parameter \rho. As in cubic open superstring field theory using the pure spinor formalism, the operator N_\rho is invertible and is equal to 1 up to a BRST-trivial quantity. So unlike the linearized equation of motion Y\bar Y QV=0 which requires truncation of the Hilbert space in order to imply QV=0, the linearized equation N_\rho QV=0 directly implies QV=0.Comment: 6 pages harvmac, added footnote and referenc

Ghost constraints and the covariant quantization of the superparticle in ten dimensions

We present a modification of the Berkovits superparticle. This is firstly in order to covariantly quantize the pure spinor ghosts, and secondly to covariantly calculate matrix elements of a generic operator between two states. We proceed by lifting the pure spinor ghost constraints and regaining them through a BRST cohomology. We are then able to perform a BRST quantization of the system in the usual way, except for some interesting subtleties. Since the pure spinor constraints are reducible, ghosts for ghosts terms are needed, which have so far been calculated up to level 4. Even without a completion of these terms, we are still able to calculate arbitrary matrix elements of a physical operator between two physical states.Comment: 38 pages, Latex, no figures. Published versio

BRST quantization of the pure spinor superstring

We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and non-minimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then proceeding to BRST quantize this system. Our analysis includes the introduction of constant ghosts and associated auxiliary fields needed to gauge fix symmetries associated with zero modes. All fields introduced in the process of quantization can be integrated out explicitly, resulting in the prescriptions for computing scattering amplitudes that have appeared previously in the literature. The zero mode insertions in the path integral follow from the integration over the constant auxiliary fields.Comment: 31 page

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

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