6,982 research outputs found
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
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
Comments on BRST quantization of strings
The BRST quantization of strings is revisited and the derivation of the path
integral measure for scattering amplitudes is streamlined. Gauge invariances
due to zero modes in the ghost sector are taken into account by using the
Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann
surfaces to quantum mechanical variables on which BRST transformations act. The
familiar ghost and antighost zero mode insertions are recovered upon
integrating out auxiliary fields. In contrast to the usual treatment, the
gauge-fixed action including all zero mode insertions is BRST invariant.
Possible anomalous contributions to BRST Ward identities due to boundaries of
moduli space are reproduced in a novel way. Two models are discussed
explicitly: bosonic string theory and topological gravity coupled to the
topological A-model.Comment: 23 pages, latex; v2: typos fixed, footnote and reference adde
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 of the conventional PS formalism is promoted to a bona fide
nilpotent charge , the cohomology of which is equivalent to the
constrained cohomology of . 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 "-ghost" field which
realizes the important relation , with 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
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
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
11D supergravity at
We compute certain spinorial cohomology groups controlling possible
supersymmetric deformations of eleven-dimensional supergravity up to order
in the Planck length. At and the spinorial
cohomology groups are trivial and therefore the theory cannot be deformed
supersymmetrically. At the corresponding spinorial cohomology
group is generated by a nontrivial element. On an eleven-dimensional manifold
such that , this element corresponds to a supersymmetric
deformation of the theory, which can only be redefined away at the cost of
shifting the quantization condition of the four-form field strength.Comment: 10 pages, 1 figure. v2: references adde
Robustness Analysis for Terminal Phases of Re-entry Flight
Advancements in the current practices used in robustness analysis for FCS design refinement by introducing a method that takes into account nonlinear effects of multiple uncertainties over the whole trajectory, to be used before robustness is finally assessed with MC analysis has been reported. Current practice in FCS robustness analysis for this kind of application mainly relies on the theory of linear time-invariant (LTI) systems. The method delivers feedback on the causes of requirement violation and adopts robustness criteria directly linked to the original mission or system requirements, such as those employed in MC analyses. The nonlinear robustness criterion proposed in the present work is based on the practical stability and/or finite time stability concepts. The practical stability property improves the accuracy in robustness evaluation with respect to frozen-time approaches, thus reducing the risk of discovering additional effects during robustness verification with Monte Carlo techniques
- …