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The lambda deformation of the pure spinor formalism of the superstring in the AdS 5 × S 5 background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its parent theory. It is also shown that the effective action takes the standard form of the Berkovits-Howe action functional, allowing to calculate the deformed background supergeometry in a straightforward way. The background fields coincide with those of the lambda model of the Green-Schwarz formalism, hence satisfying the same set of supergravity equations of motion.

The $D=11$ pure spinor superparticle has been shown to describe linearized $D=11$ supergravity in a manifestly covariant way. A number of authors have proposed that its correlation functions be used to compute amplitudes. The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions. This prescription requires the construction of ghost number one and zero vertex operators. In these notes, we construct explicitly a ghost number one vertex operator but show the incompatibiliy of a ghost number zero vertex operator satisfying a standard descent equation for $D=11$ supergravity., Comment: 13 pages

At small AdS radius, the superstring on $AdS_5\times S^5$ was conjectured by Maldacena to be equivalent to ${\cal N}=4$ super-Yang-Mills at small `t Hooft coupling where thickened Feynman diagrams can be used to compute scattering amplitudes. It was previously shown that the pure spinor worldsheet action of the $AdS_5\times S^5$ superstring can be expressed as the sum of a BRST-trivial term and a `B-term' which is antisymmetric in worldsheet derivatives. Using the explicit form of the pure spinor vertex operators, it will be argued here that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the regions near the AdS horizon. Evidence will then be presented that the antisymmetric B-term generates the super-Yang-Mills vertex so that, at small radius and arbitrary genus, the superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram expansion., Comment: 17 pages with 2 figures. Added references

The general fluctuations, in the form of vertex operators, for the type II superstring in the pure spinor formalism are considered. We review the construction of these vertex operators in flat space-time. We then review the type II superstrings in curved background in the pure spinor formalism to finally construct the vertex operators on a generic type II supergravity background., Comment: harvmac-big, 13+1 pages. Added a section

We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under SL(5). Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite-dimensional extensions of the supersymmetry algebra: the Borcherds superalgebra ${\scr B}(E_4)$, the tensor hierarchy algebra $S(E_4)$ and the exceptional superalgebra $E(5,10)$. A theorem relating ${\scr B}(E_4)$ and $E(5,10)$ to all levels is given., Comment: 14 pp. v2: minor changes, added refs

Pure spinor formalism implies that supergravity equations in space-time are equivalent to the requirement that the worldsheet sigma-model satisfies certain properties. Here we point out that one of these properties has a particularly transparent geometrical interpretation. Namely, there exists an odd nilpotent vector field on some singular supermanifold, naturally associated to space-time. All supergravity fields are encoded in this vector field, as coefficients in its normal form. The nilpotence implies, modulo some zero modes, that they satisfy the SUGRA equations of motion., LaTeX, 22pp; v2: corrected mistakes, added explanations, new Section 7; v3: we show that the nilpotence of Q implies all SUGRA equations of motion, and discuss div Q in the Introduction

The OPE between the composite $b$ ghost and the unintegrated vertex operator for massless states of the pure spinor superstring is computed and shown to reproduce the structure of the bosonic string result. The vanishing of the double pole singularity is Lorentz gauge and the single pole is shown to be equal to the corresponding integrated vertex operator., Latex, 24 pages, 1 figure. Reference added. Minor corrections

We provide a linearised superfield description of the exotic non-metric $N=(4,0)$ supergravity in $D=6$, by using a pure spinor superfield formalism. The basic field $\Psi$ is a ghost number 2 scalar, transforming in the same R-symmetry module as the tensor fields. Partial results for the $N=(3,1)$ model are presented., Comment: v2. 14 pp. Expanded version, added results on N=(3,1)

We present a novel twistor formulation of the ten-dimensional massless superparticle. This formulation is based on the introduction of pure spinor variables through a field redefinition of another model for the superparticle, and in the new description we find that the super-Pauli-Lubanski three-form naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the $D = 10$ super-Yang-Mills states., 23 pages. Fixed typos, appendix added. Published version

We construct the integrated vertex operator for the first massive states of open superstrings with $(mass)^2=1/\alpha'$ in the pure spinor formalism of the superstring theory. This vertex operator is expressed in terms of the ten dimensional $\mathcal{N}=1$ superfields describing the massive supermultiplet which appear in the unintegrated vertex operator of the same states., Comment: 29 pages, some clarifications added, matches with the published version

Elko spinors are eigenspinors of the charge conjugation operator. In this work we use the Clifford algebra of the physical space in order to formulate the theory of Elko spinors and use a procedure analog to Ryder’s derivation of Dirac equation to come up with an equation for Elko spinor fields. Unlike other works in the literature where an equation for Elko spinor fields has been studied, in this work we obtain a first order differential equation for Elko spinor fields, which resembles but is different from the Dirac equation.

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.

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.

It is well known in NSR string theory, that vertex operators can be constructed in various ``pictures''. Recently this was discussed in the context of pure spinor formalism. NSR picture changing operators have an elegant super-geometrical interpretation. In this paper we provide a generalization of this super-geometrical construction, which is also applicable to the pure spinor formalism., Comment: 14 pages, typos corrected, comments added

The full two-loop amplitudes for five massless states in Type II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and Abelian differentials on the surface. The construction combines elements from the BRST cohomology of the pure spinor formulation and from chiral splitting with the help of loop momenta and homology invariance. The α′ → 0 limit of the resulting superstring amplitude is shown to be in perfect agreement with the previously known amplitude computed in Type II supergravity. Investigations of the α′ expansion of the Type II amplitude and comparisons with predictions from S-duality are relegated to a first companion paper. A construction from first principles in the RNS formulation of the genus-two amplitude with five external NS states is relegated to a second companion paper.

We evaluate closed string disk amplitudes in the pure spinor formalism. We focus on low point functions (two- and one-point functions) but our analysis is also relevant for higher n-point functions. Amongst others we discuss issues arising due to the gauge fixing of the conformal Killing group of the disk and due to the zero mode prescription in the pure spinor formalism. As expected, in the end we find agreement with the known results from the RNS formalism., Comment: 28 pages, v2: Small changes; in particular added footnote 2 and reference [11]; version published by JHEP

An attempt is made to apply the pure spinor formalism to the non-relativistic IIA D2-brane. The fermionic constraints corresponding to the rescaled fermionic coordinates are given. Two commuting spinor fields are introduced, each one corresponding to a fermionic constraint. A BRST charge is constructed via the ansatz proposed by N. Berkovits. The nilpotency of the BRST charge leads to a set of constraints for the two spinor fields including pure spinor constraints. A novel non-trivial solution is given for one of the spinor fields which can be written as a sum of two pure spinors., Comment: 23 pages in latex, no figures; discussion added, some typos corrected, more references added

Using the pure spinor formalism for the superstring in an $AdS_5\times S^5$ background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states., Comment: 11 pages, fixed typos

We present an integrable deformation of the $AdS_{5}\times S^{5}$ pure spinor action based on homological perturbation theory. Its equations of motion, Lax connection and BRST symmetry are discussed. The resulting model describes a pure spinor superstring in a generalized supergravity background., Final version. 23 pages. Added references, improved few sentences. Version to be published in JHEP

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.

The author studies the properties and applications of quasi-Killing spinors and quasi-twistor spinors and obtains some vanishing theorems. In particular, the author classifies all the types of quasi-twistor spinors on closed Riemannian spin manifolds. As a consequence, it is known that on a locally decomposable closed spin manifold with nonzero Ricci curvature, the space of twistor spinors is trivial. Some integrability condition for twistor spinors is also obtained.

The paper clarifies some subtle points surrounding the definition of scalar curvature in generalized K$\ddot{a}$hler (GK) geometry. We have solved an open problem in GK geometry of symplectic type posed by R. Goto \cite{Go1} on relating the scalar curvature defined in terms of generalized pure spinors \emph{directly} to the underlying biHermitian structure. In particular, we apply this solution to toric GK geometry of symplectic type and prove that the scalar curvature suggested in this setting by L. Boulanger \cite{Bou} coincides with Goto's definition., A continuation of the preprints arXiv:1810.08265v1 and arXiv:1811.06848v1. 38 pages

We examine the BRS invariance of the open pure spinor superstring in the presence of background superfields on a Dp-brane. It is shown that the BRS invariance leads not only to boundary conditions on the spacetime spinors, but also to supersymmetric DBI equations of motion for the background superfields on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI equations for a D9-brane., Comment: 27 pages, typos fixed, presentation clarified, version to appear in PRD

We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized K\"ahler structures on maximal flag manifolds under $B$-transformations. We give an alternative description of the moduli space of generalized complex structures using pure spinors, and describe a cell decomposition of these moduli spaces induced by the action of the Weyl group., Comment: 29 pages. The title has been changed. Final version to appear in Journal of Geometry and Physics

In this article we present bosonic T-dualization in double space of the type II superstring theory in the pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and mathematically justified assumptions. Unlike Nikolić and Sazdović (EPJ C 77:197, 2017), where we used the first-order theory, in this article fermionic momenta are integrated out. Full T-dualization in double space is represented as a permutation of the initial $$x^\mu $$xμ and T-dual coordinates $$y_\mu $$yμ. Requiring that a T-dual transformation law of the T-dual double coordinate $${}^\star Z^M=(y_\mu ,x^\mu )$$⋆ZM=(yμ,xμ) to be of the same form as for initial one $$Z^M=(x^\mu ,y_\mu )$$ZM=(xμ,yμ), we obtain the form of the T-dual background fields in terms of the initial ones. The advantage of using the action with integrated fermionic momenta is that it gives all T-dual background fields in terms of the initial ones. In the case of the first-order theory Nikolić and Sazdović (2017) a T-dual R-R field strength was obtained out of the double space formalism under additional assumptions.

In this article we consider simultaneous T-dualization of type II superstring action in pure spinor formulation. Simultaneous T-dualization means that we make T-dualization at the same time along some subset of initial coordinates marked by $x^a$. The only imposed assumption stems from the applicability of the Buscher T-dualization procedure - background fields do not depend on dualized directions $x^a$. In this way we obtain the full form of the T-dual background fields and T-dual transformation laws. Because two chiral sectors transform differently, there are two sets of vielbeins and gamma matrices connected by the local Lorentz transformation. Its spinorial representation is the same as in the constant background case. We also found the full expression for T-dual dilaton field., Comment: Comments on dilaton transformation added

In this work, a solution linear in the momentum for the massless constraint $P^{m}P_{m}=0$ is investigated. It is presented in terms of a $SO(2n,\mathbb{C})$ to $U(n)$ decomposition and interpreted in terms of projective pure spinors, which are known to parametrize the $\tfrac{SO(2n)}{U(n)}$ coset. The worldline action is quantized using the BRST formalism and, using the results of Berkovits and Cherkis, the ghost number zero wave function is shown to generate massless solutions for field equations of arbitrary spin. The model can be covariantly expressed by the action recently proposed in $D=10$ by Berkovits, in terms of a twistor-like constraint. However, a thorough account of its gauge symmetries does not lead to a spacetime supersymmetric theory. In order to derive from first principles the superparticle in the pure spinor formalism, a new model is proposed with partial worldline supersymmetry. The gauge algebra is then analyzed within the Batalin-Vilkovisky formalism and the gauge fixed action is finally shown to describe the pure spinor superparticle times a $U(1)$ decoupled sector., Comment: 20 pages. Small clarification added to the published version

In this work we give an explicit construction for the vertex operators of massless states in the pure spinor superstring in a plane wave background. The construction is based on the observation that the full action can be divided in two parts, where the simpler one is based on a smaller coset and closely resembles the gauge fixed Green-Schwarz action., Comment: Latex, 28 pages

The $b$-ghost of the pure spinor formalism in a general curved background is not holomorphic. For such theories, the construction of the string measure requires the knowledge of the action of diffeomorphisms on the BV phase space. We construct such an action for the pure spinor sigma-model in $AdS_5\times S^5$. From the point of view of the BV formalism, this sigma-model belongs to the class of theories where the expansion of the Master Action in antifields terminates at the quadratic order. We show that it can be reduced to a simpler degenerate sigma-model, preserving the AdS symmetries. We construct the action of the algebra of worldsheet vector fields on the BV phase space of this minimalistic sigma-model, and explain how to lift it to the original model., 35pp. LaTeX; v2,3,4: corrections, improved presentation, v5: added Section 5.4 (gluing the BV phase space from charts) and Section 6, v6: published version with minor corrections

Using non-minimal pure spinor superspace, Cederwall has constructed BRST-invariant actions for $D=10$ super-Born-Infeld and $D=11$ supergravity which are quartic in the superfields. But since the superfields have explicit dependence on the non-minimal pure spinor variables, it is non-trivial to show these actions correctly describe super-Born-Infeld and supergravity. In this paper, we expand solutions to the equations of motion from Cederwall's actions to leading order around the linearized solutions and show that they correctly describe the interactions of $D=10$ super-Born-Infeld and $D=11$ supergravity., 20 pages. Added reference to paper of Chang, Lin, Wang and Yin

We analyze general $$ \mathcal{N}=2 $$ N = 2 supersymmetric AdS4 solutions of type IIB supergravity. Utilizing a set of pure spinor equations directly adapted to $$ \mathcal{N}=2 $$ N = 2 , the necessary and sufficient conditions for supersymmetry are reduced to a concise system of partial differential equations for two functions which determine the solutions. We show that using this system analytic solutions can be generated, thus potentially expanding the rather limited set of known AdS4 solutions in type IIB supergravity.

The $D=11$ pure spinor formulation of the superparticle allows a simple realization of covariant quantization, unlike the $D=11$ Brink-Schwarz-like superparticle. We explicitly show the equivalence between the cohomologies of these two models in the context of two different group decompositions: $SO(10,1) \rightarrow SO(1,1)\times SO(9)$ and $SO(10,1) \rightarrow SO(3,1)\times SO(7)$. We also carry out a light-cone analysis of the pure spinor cohomology, and show that it correctly reproduces the $SO(9)$ equations of motion for $D=11$ linearized supergravity., 24 pages. Fixed typos and added footnote

We provide the covariant superspace equations that are sufficient to determine the complete $\theta$ expansion of the vertex operator of the open string massive states with $(mass)^2=1/\alpha'$ 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 $\theta$ expansion of the superfields appearing in the unintegrated vertex to $O(\theta^3)$. Finally, we compute the contribution to a 3-point tree amplitude with the resulting vertex operator upto $O(\theta^3)$ and find its kinematic structure to be identical to the corresponding RNS computation., Comment: 32 pages

Same amplitudes evaluated independently using RNS and pure spinor formalism are expected to agree. While for massless states, this fact has been firmly established, for massive states such an explicit check has been lacking so far. We compute all massless-massless-massive 3-point functions in open supertrings in pure spinor formalism for the first massive states and compare them with the corresponding RNS results. We fix the normalization of the vertex operators of the massive states by comparing same set of 3-point functions for a fixed ordering in the two formalisms. Once fixed, the subsequent 3-point functions for each inequivalent ordering match exactly. This extends the explicit demonstration of equivalence of pure spinor and RNS formalism from massless states to first massive states., Comment: 33 pages

In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to supergravity amplitudes as a byproduct. At six points, the sources of the hexagon anomaly are identified in superspace as systematic obstructions to BRST invariance. Our results are expected to reproduce any integrated SYM amplitude in dimensions $D< 8$.

We showed in previous work that for homogeneous Yang-Baxter (YB) deformations of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the closed string density $e^{-2 \Phi} \sqrt{g}$, remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE, or $\eta$-deformation, we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We give a physical meaning to the Killing vector $I$ of generalized supergravity and show for all YB deformations: 1) $I$ appears as a current for center of mass motion on the worldvolume of a D-branes probing the background, 2) $I$ is equal to the divergence of the noncommutativity parameter, 3) $I$ exhibits "holographic" behavior, where the radial component of $I$ vanishes at the AdS boundary, and 4) in pure spinor formalism $I$ is related to a certain state in the BRST cohomology., Comment: 11 pages, 2 column; v2 references updated; v3 to appear in EPJC

Open supermembrane with a constant three-form flux in the pure spinor formalism is examined. The BRST symmetry of the open supermembrane action leads to non-commutative (NC) M-branes. In addition to the NC M5-brane with a self-dual two-form flux, we find a NC M9-brane with an electric flux and a NC M9-brane with a magnetic flux. The former reduces in the critical electric flux limit to an M2-brane on the M9-brane, while the latter reduces in the strong magnetic flux limit to infinitely many Kaluza-Klein monopoles dissolved into the M9-brane. These NC M-branes are shown to preserve a half of 32 supersymmetries., 17 pages, published version

D=4, N=4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D=10 theory. That superspace, in particular the choice of pure spinor variables, is less suitable for dealing with fields that are inherently 4-dimensional, such as the superfields based on the scalars, which are gauge-covariant, and traces of powers of scalars, which are gauge-invariant. We give a reformulation of D=4, N=4 super-Yang-Mills theory in N=4 superspace, using inherently 4-dimensional pure spinors. All local degrees of freedom reside in a superfield based on the physical scalars. The formalism should be suited for calculations of correlators of traces of scalar superfields., 13 pp

A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor superparticle by requiring that $\{Q , b\} = T$ where $Q = \Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ 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 $\bar{\Sigma}^{i}$ constructed out of the fermionic spinor $D_{\alpha}$ and pure spinor variables. This simplified version will be shown to satisfy $\{Q, b\} = T$ and $\{b , b\} =$ BRST - trivial., Comment: 47 pages. Added references

The integrated massless vertex operator in an $AdS_5\times S^5$ background in the pure spinor formalism is constructed in terms of superfields., Comment: 22 pages, latex. Fixed discussion on gauge invariant vertex operators

We study the geometric properties of a $(2m+1)$-dimensional complex manifold $\mathcal{M}$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset \mathrm{Spin}(2m+1,\mathbb{C})$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $\mathcal{M}$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $\xi$ up to scale. The defining property of $\xi$ is that it determines an almost null structure, i.e.\ an $m$-plane distribution $\mathcal{N}_\xi$ along which $g$ is totally degenerate. We develop a spinor calculus, by means of which we encode the geometric properties of $\mathcal{N}_\xi$ and of its rank-$(m+1)$ orthogonal complement $\mathcal{N}_\xi^\perp$ corresponding to the algebraic properties of the intrinsic torsion of the $P$-structure. This is the failure of the Levi-Civita connection $\nabla$ of $g$ to be compatible with the $P$-structure. In a similar way, we examine the algebraic properties of the curvature of $\nabla$. Applications to spinorial differential equations are given. Notably, we relate the integrability properties of $\mathcal{N}_\xi$ and $\mathcal{N}_\xi^\perp$ 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 $(\mathcal{M},g)$ has prescribed curvature. We discuss applications of this work to the study of real pseudo-Riemannian manifolds., Comment: Odd-dimensional version of arXiv:1212.3595 v2: Presentation improved. A number of corrections made: diagrams describing the curvature and intrinsic torsion classification; Geometric interpretation of spinorial equations; some errors in formulae now fixed. Some material regarding parallel spinors removed (to be including in a separate article) v3: as published

In this chapter, we will begin by investigating the fermionic analog of the notion of quantization, which takes functions of anticommuting variables on a phase space with symmetric bilinear form \((\cdot ,\cdot )\) and gives an algebra of operators with generators satisfying the relations of the corresponding Clifford algebra.

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.

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., LaTex, 37 pages, references added, match published version in Journal of High Energy Physics, 2016

All solutions of the Einstein equations admitting super-covariantly constant spinors in the sense of Gibbons and Hull are found. There are two classes corresponding to stationary charged dust and plane waves with dust respectively.

A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group. Covariance under generalised super-diffeomorphisms is manifest. Ordinary superspace is obtained as a solution of the orthosymplectic section condition. A systematic study of curved superspace Bianchi identities is performed, and a relation to a double pure spinor superfield cohomology is established. A Ramond-Ramond superfield is constructed as an infinite-dimensional orthosymplectic spinor. Such objects in minimal orbits under the OSp supergroup ("pure spinors") define super-sections., Comment: 28 pp., plain tex. v2: refs. added

The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators $j_{BRST}$ and composite $b$ ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor $j_{BRST}+b$, the worldsheet variables combine into N=1 worldsheet superfields $X^m$ and $\Theta^\alpha$ together with a superfield constraint relating $DX^m$ and $D\Theta^\alpha$. The constraint implies that the worldsheet superpartner of $\theta^\alpha$ is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formalisms, as well as a new twistor-string formalism with manifest N=1 worldsheet supersymmetry. These N=1 worldsheet methods generalize in curved Ramond-Ramond backgrounds, and a manifestly N=1 worldsheet supersymmetric action is proposed for the superstring in an $AdS_5\times S^5$ background in terms of the twistor superfields. This $AdS_5\times S^5$ worldsheet action is a remarkably simple fermionic coset model with manifest $PSU(2,2|4)$ symmetry and might be useful for computing $AdS_5\times S^5$ superstring scattering amplitudes., Comment: 30 pages. Corrected typos, added 2 footnotes, and dedicated paper to Mario Tonin

We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of conformal Killing vectors and twistor spinors and play important roles in supersymmetric field theories in conformal backgrounds are extended to more general superalgebras by using the graded Lie algebra structure of conformal Killing-Yano forms and the symmetry operators of twistor spinors. The even part of the extended conformal superalgebra corresponds to conformal Killing-Yano forms and the odd part consists of twistor spinors., 16 pages, published version

In this work, some aspects of the ambitwistor pure spinor string are investigated. The $b$ ghost is presented and its main properties are derived in a simple way, very similar to the usual pure spinor $b$ ghost construction. The heterotic case is also addressed with a new proposal for the BRST charge. The BRST cohomology is shown to correctly describe the heterotic supergravity spectrum and a semi-composite $b$ ghost is constructed., 23 pages, reference and clarifications added, typos fixed. Published version

Indexación: Web of Science We investigate the complex of differential forms in curved, six-dimensional, N = (1, 0) superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group arises on a pure spinor subspace of the cotangent space. The p-forms are defined by super-Weylcovariant tensor fields on this pure spinor subspace. The on-shell dynamics of such fields is superconformal. We construct the superspace de Rham complex by successively obstructing the closure of forms. We then extend the analysis to composite forms obtained by wedging together forms of lower degree. Finally, we comment on applications to integration in curved superspace and propose a superspace formulation of the abelian limit of the non-abelian tensor hierarchy of N = (1, 0) superconformal models. http://link.springer.com/article/10.1007%2FJHEP05%282016%29016#aboutarticle