Pure Spinor Research Articles

Theta expansion of first massive vertex operator in pure spinor

We provide the covariant superspace equations that are sufficient to determine the complete θ expansion of the vertex operator of the open string massive states with (mass)2 = 1/α′ in pure spinor formalism of superstring theory. These equations get rid of the redundant degrees of freedom in superfields and are consistent with the BRST conditions derived in [1]. Further, we give the explicit θ expansion of the superfields appearing in the unintegrated vertex to O(θ3). Finally, we compute the contribution to a 3-point tree amplitude with the resulting vertex operator upto O(θ3) and find its kinematic structure to be identical to the corresponding RNS computation.

Plane-wave背景上の超弦理論のdouble spinor形式

Plane-wave背景上の超弦理論のdouble spinor形式

Spinorially Twisted Spin Structures, III: CR Structures

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin $$^{c, r}$$ structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds, and Sasakian manifolds. Finally, we study hypersurfaces of Kahler manifolds via partially pure Spin $$^c$$ spinors.

All-spin-based ultrafast nanologic elements with aNi4cluster

Starting from high-level ab initio calculations, we present ultrafast spin dynamical effects and all-spin-based nanologic elements on a ${\mathrm{Ni}}_{4}$ cluster. The predominant underlying mechanisms for our operations are optically induced coherent $\mathrm{\ensuremath{\Lambda}}$ processes, the optimized parameters of which are obtained from a dedicated genetic algorithm search. The geometry of the cluster exhibits a high degree of spin localization. Thus, maneuvering the spin localizations we construct a pure-spin OR gate. Additionally, functional intramolecular cooperative effects such as spin bifurcation and spin merging are introduced that facilitate the setup of the latter. In the which-path information effect the phase of the final spin state is exploited to reveal the path traveled by the spin in a two-step spin transfer scenario. This is beneficial for both classical and quantum computations on small spatial and temporal scales.

Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models

It is well known that instantons are classical topological solutions existing in the context of quantum field theories that lie behind the standard model of particles. To provide a better understanding for the dynamical nature of spinor-type instanton solutions, conformal invariant pure spinor fermionic models that admit particle-like solutions for the derived classical field equations are studied in this work under cosine wave forcing. For this purpose, the effects of external periodic forcing on two systems that have different dimensions and quantum spinor numbers and have been obtained under the use of Heisenberg ansatz are investigated by constructing their Poincare sections in phase space. As a result, bifurcations and chaos are observed depending on the excitation amplitude of the external forcing in both pure spinor fermionic models.

A Projective-to-Conformal Fefferman-Type Construction

We study a Fefferman-type construction based on the inclusion of Lie groups ${\rm SL}(n+1)$ into ${\rm Spin}(n+1,n+1)$. The construction associates a split-signature $(n,n)$-conformal spin structure to a projective structure of dimension $n$. We prove the existence of a canonical pure twistor spinor and a light-like conformal Killing field on the constructed conformal space. We obtain a complete characterisation of the constructed conformal spaces in terms of these solutions to overdetermined equations and an integrability condition on the Weyl curvature. The Fefferman-type construction presented here can be understood as an alternative approach to study a conformal version of classical Patterson-Walker metrics as discussed in recent works by Dunajski-Tod and by the authors. The present work therefore gives a complete exposition of conformal Patterson-Walker metrics from the viewpoint of parabolic geometry.

Connecting the ambitwistor and the sectorized heterotic strings

The sectorized description of the (chiral) heterotic string using pure spinors has been misleadingly viewed as an infinite tension string. One evidence for this fact comes from the tree level 3-point graviton amplitude, which we show to contain the usual Einstein term plus a higher curvature contribution. After reintroducing a dimensionful parameter ℓ in the theory, we demonstrate that the heterotic model is in fact two-fold, depending on the choice of the supersymmetric sector, and that the spectrum also contains one massive (open string like) multiplet. By taking the limit ℓ → ∞, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner’s RNS description.

A superfield realization of the integrated vertex operator in an AdS5 \xd7 S5 background

The integrated massless vertex operator in an AdS5 × S5 background in the pure spinor formalism is constructed in terms of superfields.

Generalized almost product structures and generalized CRF-structures

We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for generalized CRF-structure and investigate the resulting decomposition of the de Rham operator. As applications we give a characterization of generalized complex manifolds that are locally the product of generalized complex factors and discuss infinitesimal deformations of generalized CRF-structures.

Simplified D = 11 pure spinor b ghost

A b-ghost was constructed for the D = 11 non-minimal pure spinor superparticle by requiring that {Q, b} = T where Q={Lambda}^{alpha }{D}_{alpha }+{R}^{alpha }{overline{W}}_{alpha } is the usual non-minimal pure spinor BRST operator. As was done for the D = 10 b-ghost, we will show that the D = 11 b-ghost can be simplified by introducing an SO(10, 1) fermionic vector {overline{Sigma}}^i constructed out of the fermionic spinor Dα and pure spinor variables. This simplified version will be shown to satisfy {Q, b} = T and {b, b} = BRST - trivial.

Ambitwistor superstring in the Green\u2013Schwarz formulation

In this paper we construct the ambitwistor superstring in the Green–Schwarz formulation. The model is obtained from the related pure spinor version. We show that the spectrum contains only ten-dimensional supergravity and that kappa symmetry in a curved background implies some of the standard constraints.

Pure spinors, intrinsic torsion and curvature in odd dimensions

We study the geometric properties of a (2m+1)-dimensional complex manifold M admitting a holomorphic reduction of the frame bundle to the structure group P⊂Spin(2m+1,C), the stabiliser of the line spanned by a pure spinor at a point. Geometrically, M is endowed with a holomorphic metric g, a holomorphic volume form, a spin structure compatible with g, and a holomorphic pure spinor field ξ up to scale. The defining property of ξ is that it determines an almost null structure, i.e. an m-plane distribution Nξ along which g is totally degenerate.We develop a spinor calculus, by means of which we encode the geometric properties of Nξ and of its rank-(m+1) orthogonal complement Nξ⊥ corresponding to the algebraic properties of the intrinsic torsion of the P-structure. This is the failure of the Levi-Civita connection ∇ of g to be compatible with the P-structure. In a similar way, we examine the algebraic properties of the curvature of ∇.Applications to spinorial differential equations are given. Notably, we relate the integrability properties of Nξ and Nξ⊥ to the existence of solutions of odd-dimensional versions of the zero-rest-mass field equation. We give necessary and sufficient conditions for the almost null structure associated to a pure conformal Killing spinor to be integrable. Finally, we conjecture a Goldberg–Sachs-type theorem on the existence of a certain class of almost null structures when (M,g) has prescribed curvature.We discuss applications of this work to the study of real pseudo-Riemannian manifolds.

T-dualization of type II superstring theory in double space

In this article we offer a new interpretation of the T-dualization procedure of type II superstring theory in the double space framework. We use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms. T-dualization along any subset of the initial coordinates, x^a, is equivalent to the permutation of this subset with subset of the corresponding T-dual coordinates, y_a, in double space coordinate Z^M=(x^mu ,y_mu ). Requiring that the T-dual transformation law after the exchange x^aleftrightarrow y_a has the same form as the initial one, we obtain the T-dual NS–NS and NS–R background fields. The T-dual R–R field strength is determined up to one arbitrary constant under some assumptions. The compatibility between supersymmetry and T-duality produces a change of bar spinors and R–R field strength. If we dualize an odd number of dimensions x^a, such a change flips type IIA/B to type II B/A. If we T-dualize the time-like direction, one imaginary unit i maps type II superstring theories to type hbox {II}^star ones.

Fermionic T-duality in fermionic double space

In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is represented as permutation of the fermionic coordinates θα and θ¯α with the corresponding fermionic T-dual ones, ϑα and ϑ¯α, respectively. Demanding that T-dual transformation law has the same form as initial one, we obtain the known form of the fermionic T-dual NS–R and R–R background fields. Fermionic T-dual NS–NS background fields are obtained under some assumptions. We conclude that only symmetric part of R–R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms.

Master symmetry in the AdS5 \xd7 S5 pure spinor string

We lift the set of classical non-local symmetries recently studied by Klose, Loebbert, and Münkler in the context of ℤ2 cosets to the pure spinor description of the superstring in the AdS5 × S5 background.

Twistor Parametrization of Locally BPS Super-Wilson Loops

We consider the kinematics of the locally BPS super-Wilson loop in N=4 super-Yang-Mills with scalar coupling from a twistorial point of view. We find that the kinematics can be described either as supersymmetrized pure spinors or as a point in the product of two super-Grassmannian manifolds G2∣2(4∣4)×G2∣2(4∣4). In this description of the kinematics the scalar–scalar correlation function appearing in the one-loop evaluation of the super-Wilson loop can be neatly written as a sum of four superdeterminants.

Removable Presymplectic Singularities and the Local Splitting of Dirac Structures

We call a singularity of a presymplectic form $\omega$ removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of singularities is given in terms of regularizing functions for pure spinors. All removable singularities are poles in the sense that the norm of $\omega$ is not locally bounded. The points at which removable singularities occur are the non-regular points of the Dirac structure for which we prove a general splitting theorem: Locally, every Dirac structure is the gauge transform of the product of a tangent bundle and the graph of a Poisson structure. This implies that in a neighborhood of a removable singularity $\omega$ can be split into a non-singular presymplectic form and a singular presymplectic form which is the partial inverse of a Poisson bivector that vanishes at the singularity. An interesting class of examples is given by log-Dirac structures which generalize log-symplectic structures. The analogous notion of removable singularities of Poisson structures is also studied.

D-branes from pure spinor superstring in AdS5 × S5 background

We examine the surface term for the BRST transformation of the open pure spinor superstring in an AdS5×S5 background. We find that the boundary condition to eliminate the surface term leads to a classification of possible configurations of 1/2 supersymmetric D-branes.

Exploring the lambda model of the hybrid superstring

The purpose of this contribution is to initiate the study of integrable deformations for different superstring theory formalisms that manifest the property of (classical) integrability. In this paper we choose the hybrid formalism of the superstring in the background AdS_{2}xS^{2} and explore in detail the most immediate consequences of its lambda-deformation. The resulting action functional corresponds to the lambda-model of the matter part of the fairly more sophisticated pure spinor formalism, which is also known to be classical integrable. In particular, the deformation preserves the integrability and the one-loop conformal invariance of its parent theory, hence being a marginal deformation.

On-shell type II supergravity from the ambitwistor pure spinor string

We obtain all the type II supergravity constraints in the pure spinor ambitwistor string by imposing consistency of local worldsheet gauge symmetries.