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

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

Pure spinor computation towards open string three-loop

Using the recent results in the pure spinor formulation, we lay out a ground-work towards the full momentum space amplitudes of open superstrings at three-loop. After briefly reviewing the one-loop amplitude, we directly work out the two-loop and reproduce the result that was obtained by a symmetry argument. For the three-loop, first we use the two-loop regulator as a warm-up exercise. The result vanishes. We then employ the regulator that has been recently proposed by Aisaka and Berkovits (AB). It is noted that the terms in higher power in $\frac{1}{\lambda\bar{\lambda}}$ that render the two-loop regulator disqualified for the three-loop do not contribute. This with a few other indications suggests a possibility that the AB regulator might also lead to a vanishing result. Nevertheless, we argue that it is possible to acquire the three-loop amplitude, and present a result that we anticipate to be the three-loop amplitude.Comment: 41 pages, latex, cosmetic change

Estimation of GRB detection by FiberGLAST

FiberGLAST is one of several instrument concepts being developed for possible inclusion as the primary Gamma-ray Large Area Space Telescope (GLAST) instrument. The predicted FiberGLAST effective area is more than 12,000 cm2 for energies between 30 MeV and 300 GeV, with a field of view that is essentially flat from 0°–80°. The detector will achieve a sensitivity more than 10 times that of EGRET. We present results of simulations that illustrate the sensitivity of FiberGLAST for the detection of gamma-ray bursts

The Classical Exchange Algebra of AdS5 x S5 String Theory

The classical exchange algebra satisfied by the monodromy matrix of AdS5 x S5 string theory in the Green-Schwarz formulation is determined by using a first-order Hamiltonian formulation and by adding to the Bena-Polchinski-Roiban Lax connection terms proportional to constraints. This enables in particular to show that the conserved charges of this theory are in involution. This result is obtained for a general world-sheet metric. The same exchange algebra is obtained within the pure spinor description of AdS5 x S5 string theory. These results are compared to the one obtained by A. Mikhailov and S. Schaefer-Nameki for the pure spinor formulation.Comment: 37 pages; v2: Result on Jacobi identity and Yang-Baxter equation added in section 3.3; v3: References added; v4: Comparison with ref [12] clarified in section 3.

Superstring in the plane-wave background with RR flux as a conformal field theory

We study the type IIB superstring in the plane-wave background with Ramond-Ramond flux and formulate it as an exact conformal field theory in operator formalism. One of the characteristic features of the superstring in a consistent background with RR flux, such as the AdS5xS5 and its plane-wave limit, is that the left- and the right-moving degrees of freedom on the worldsheet are inherently coupled. In the plane-wave case, it is manifested in the well-known fact that the Green-Schwarz formulation of the theory reduces to that of free massive bosons and fermions in the light-cone gauge. This raises the obvious question as to how this feature is reconciled with the underlying conformal symmetry of the string theory. By adopting the semi-light-cone conformal gauge, we will show that, despite the existence of such non-linear left-right couplings, one can construct two independent sets of quantum Virasoro operators in terms of fields obeying the free-field commutation relations. Furthermore, we demonstrate that the BRST cohomology analysis reproduces the physical spectrum obtained in the light-cone gauge.Comment: 37 pages, Latex, no figure; published versio

The Structure of n-Point One-Loop Open Superstring Amplitudes

In this article we present the worldsheet integrand for one-loop amplitudes in maximally supersymmetric superstring theory involving any number n of massless open string states. The polarization dependence is organized into the same BRST invariant kinematic combinations which also govern the leading string correction to tree level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang Mills theory and on the other hand the color tensors at quadratic alpha prime order of the color dressed tree amplitude.Comment: 75 pp, 8 figs, harvmac TeX, v2: published versio

Scattering equations, supergravity integrands, and pure spinors

The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version of this theory, we give a prescription for computing correlators on higher genus worldsheets which manifest spacetime supersymmetry. These correlators are conjectured to provide the loop integrands of supergravity scattering amplitudes, supported on the scattering equations. We give nontrivial evidence in support of this conjecture at genus one and two with four external states. Throughout, we find a close correspondence with the pure spinor formalism of superstring theory, particularly regarding regulators and zero-mode counting