Showing papers on "Superspace published in 2010"
TL;DR: In this paper, it was shown that all scattering amplitudes in the maximally supersymmetric N = 4 super-Yang-Mills theory possess dual superconformal symmetry.
839 citations
TL;DR: In this article, all semi-symmetric cosets which have zero beta function and central charge c ≤ 26 at one loop in perturbation theory are described by integrable sigma-models.
Abstract: Several string backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. Their target space is always a \( {\mathbb{Z}_4} \) supercoset (a semi-symmetric superspace). Here we list all semi-symmetric cosets which have zero beta function and central charge c ≤ 26 at one loop in perturbation theory.
173 citations
TL;DR: In this article, an N = 1, D = 4 superspace with the superconformal algebra as the structure group was constructed and discussed its relation to prior component approaches and the existing Poincare superspaces.
144 citations
TL;DR: In this paper, the 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction in superspace.
Abstract: 6 dimensional maximal super Yang-Mills on-shell amplitudes are formulated in superspace using 6 dimensional spinors. The 3,4,5-point tree amplitudes are obtained by supersymmetrizing their bosonic counterparts and confirmed through the BCFW construction. In contrast to 4 dimensions this superspace is non-chiral, reflecting the fact that one cannot differentiate MHV from \( \overline {\text{MHV}} \) in 6 dimensions. Combined with unitarity methods, this superspace should be useful for the study of multi-loop D dimensional maximal super Yang-Mills and gravity amplitudes. Furthermore, the non-chiral nature gives a natural framework for an off-shell construction. We show this by matching our result with off-shell D=4 N=4 super Yang-Mills amplitudes, expressed in projective superspace.
118 citations
TL;DR: In this paper, the authors investigated the Yangian symmetry of scattering amplitudes in the super Yang-Mills theory and showed that its formulations in twistor and momentum twistor space can be interchanged.
Abstract: We investigate the Yangian symmetry of scattering amplitudes in $$ \mathcal{N} = 4 $$ super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged. In particular we show that the full symmetry can be thought of as the Yangian of the dual superconformal algebra, annihilating the amplitude with the MHV part factored out. The equivalence of this picture with the one where the ordinary superconformal symmetry is thought of as fundamental is an algebraic expression of Tduality. Motivated by this, we analyse some recently proposed formulas, which reproduce different contributions to amplitudes through a Grassmannian integral. We prove their Yangian invariance by directly applying the generators.
117 citations
TL;DR: In this paper, the supersymmetric massless five-point amplitude at tree-level was obtained using the pure spinor formalism and the equivalence of an OPE identity in string theory with a subset of the Bern-Carrasco-Johansson five point kinematic relations.
Abstract: We use the pure spinor formalism to obtain the supersymmetric massless five-point amplitude at tree-level in a streamlined fashion. We also prove the equivalence of an OPE identity in string theory with a subset of the Bern-Carrasco-Johansson five-point kinematic relations, and demonstrate how the remaining BCJ identities follow from the different integration regions over the open string world-sheet, therefore providing a first principles derivation of the (supersymmetric) BCJ identities.
102 citations
TL;DR: A new kappa-invariant massless superparticle model providing a dynamical realization of the Maxwell superalgebra is proposed, using the techniques of nonlinear coset realization to the Maxwellsupergroup.
Abstract: We present the Maxwell superalgebra, an N=1, D=4 algebra with two Majorana supercharges, obtained as the minimal enlargement of a Poincare superalgebra containing the Maxwell algebra as a subalgebra. The new superalgebra describes the supersymmetries of generalized N=1, D=4 superspace in the presence of a constant Abelian supersymmetric field strength background. Applying the techniques of nonlinear coset realization to the Maxwell supergroup we propose a new {kappa}-invariant massless superparticle model providing a dynamical realization of the Maxwell superalgebra.
102 citations
TL;DR: In this article, it was shown that the four and six-point tree-level amplitudes of ABJM enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3.
Abstract: We demonstrate that the four and six-point tree-level amplitudes of N=6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.
100 citations
TL;DR: In this article, the authors used supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions, and showed that the three-point amplitude vanishes on-shell.
Abstract: We use supertwistor space to construct scattering amplitudes of maximal superconformal theories in three and six dimensions. In both cases, the constraints of superconformal invariance and rationality imply that the three-point amplitude vanishes on-shell, which constrains the four-point amplitude to have vanishing residues in all channels. In three dimensions, we nd a unique solution for the four-point amplitude and demonstrate that it agrees with the component result in the BLG theory. This suggests that BLG is the unique three-dimensional theory with classical OSp(8|4) symmetry that admits a Lagrangian
description. We also show that one can derive the four-point amplitude of the ABJM theory from our N = 8 result by reducing the supersymmetry, which implies that
the tree-level Yangian symmetry recently found in ABJM is also present in BLG. In six dimensions, we find that the consistency conditions imply that all tree-level amplitudes
vanish. This leads us to conjecture that an interacting six-dimensional theory with classical OSp(8|4) symmetry does not have a Lagrangian description, local or nonlocal, unless the (2, 0) tensor multiplets are supplemented by additional degrees of freedom.
96 citations
TL;DR: In this paper, the authors present formulae for the calculation of Dirac gaugino masses at leading order in the supersymmetry breaking scale using the methods of analytic continuation in superspace and demonstrate a link with kinetic mixing.
91 citations
TL;DR: In this article, the Fayet-Iliopoulos term was used to describe the N = 1 supersymmetric Born-Infeld action for self-dual nonlinear supersymetric electrodynamics, and a two-parameter duality-covariant deformation of this action was proposed for partial breaking of N = 2 supersymmetry.
Abstract: The N=1 supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken N=2 rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the Fayet-Iliopoulos term without losing the second nonlinearly realized supersymmetry. Although the first supersymmetry then becomes spontaneously broken, the deformed action still describes partial N=2{yields}N=1 supersymmetry breaking. The unbroken supercharges in this theory correspond to a different choice of N=1 subspace in the N=2 superspace, as compared with the undeformed case. Implications of the Fayet-Iliopoulos term for general models for self-dual nonlinear supersymmetric electrodynamics are discussed. The known ubiquitous appearance of the Volkov-Akulov action in such models is explained. We also present a two-parameter duality-covariant deformation of the N=1 supersymmetric Born-Infeld action as a model for partial breaking of N=2 supersymmetry.
TL;DR: In this article, a four-loop spectrum of single trace operators in the SU(2) × SU (2) sector of ABJM and ABJ supersymmetric Chern-Simons theories is computed using superspace techniques.
Abstract: Using \( \mathcal{N} = 2 \) superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) × SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h2(λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h2(λ) that interpolates between weak and strong couplings.
TL;DR: Project is a projective supersymmetry approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkahler and quaternionic Kahler metrics as discussed by the authors.
Abstract: N = 2 supersymmetry in four space-time dimensions is intimately re- lated to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hy- perkahler manifolds. On the other hand, when coupled to N = 2 supergrav- ity, the sigma-model target spaces must be quaternionic Kahler. It is known that such manifolds of restricted holonomy are dicult to generate explic- itly. Projective superspace is a eld-theoretic approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkahler and quaternionic Kahler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.
TL;DR: In this paper, a supersymmetry-without-supersymmetry approach is presented to calculate averages over ratios of characteristic polynomials, without actually mapping onto superspaces.
Abstract: There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can call our approach 'supersymmetry without supersymmetry' because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.
01 Jan 2010
TL;DR: Aspects of the D = 4, N = 4 superconformal symmetry relevant to the AdS/CFT duality and integrability are reviewed in this paper.
Abstract: Aspects of the D = 4, N = 4 superconformal symmetry relevant to the AdS/CFT duality and integrability are reviewed. These include the Lie superalgebra psu(2; 2j4), its representations, conformal transformations and correlation functions in N = 4 super Yang{Mills theory as well as an illustration of the AdS5 S 5 superspace on which the dual string theory is formulated.
TL;DR: The relation between supersymmetric σ-models on hyperkahler manifolds, projective superspace, and twistor space has been studied in this paper, where the authors present a coherent picture with a number of new results.
Abstract: We describe the relation between supersymmetric σ-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.
TL;DR: In this article, a zero-curvature Lax connection was constructed in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3)/SO(1,3) supercoset sigma-model.
Abstract: We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.
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TL;DR: The first six chapters give an introduction to supersymmetry in four spacetime dimensions, they fill about two thirds of the lecture notes and are in principle self-contained as discussed by the authors.
Abstract: These lectures on supersymmetry and extra dimensions are aimed at finishing undergraduate and beginning postgraduate students with a background in quantum field theory and group theory. Basic knowledge in general relativity might be advantageous for the discussion of extra dimensions. This course was taught as a 24+1 lecture course in Part III of the Mathematical Tripos in recent years. The first six chapters give an introduction to supersymmetry in four spacetime dimensions, they fill about two thirds of the lecture notes and are in principle self-contained. The remaining two chapters are devoted to extra spacetime dimensions which are in the end combined with the concept of supersymmetry. Videos from the course lectured in 2006 can be found online at http://www.sms.cam.ac.uk/collection/659537 .
TL;DR: In this article, it was shown that the four and six-point tree-level amplitudes of ABJM enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP^3.
Abstract: We demonstrate that the four and six-point tree-level amplitudes of N = 6 superconformal Chern-Simons theory (ABJM) enjoy OSp(6|4) dual superconformal symmetry if one enlarges the dual superspace to include three additional Grassmann-even coordinates which correspond to an abelian isometry of CP^3. The inclusion of these coordinates enables us to match the nontrivial dual superconformal generators with level-one Yangian generators when acting on on-shell amplitudes. We also discuss some implications of dual conformal symmetry for loop-level amplitudes.
TL;DR: In this article, a zero-curvature Lax connection is constructed in a sub-sector of the superstring theory on AdS4 × CP3 which is not described by the OSp(6|4)/U(3) × SO(1, 3) supercoset sigma-model.
Abstract: We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS4 × CP3 which is not described by the OSp(6|4)/U(3) × SO(1, 3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.
TL;DR: In this article, the authors compute the coefficient of the massless two-loop four-point amplitude from first principles in the pure spinor superspace formalism, where unknown normalizations of chiral determinant formulae force the coefficient to be determined only indirectly through factorization.
Abstract: Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formulae force the two-loop coefficient to be determined only indirectly through factorization, the computation in the pure spinor formalism can be smoothly carried out.
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TL;DR: In this article, it has been shown that given a point and a velocity in conformal superspace, the Einstein equations generate a unique curve in the conformal superspaces.
Abstract: It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the Einstein constraints has an unexpected extra symmetry. This allows us to complete the project. We show that given a point and a velocity in conformal superspace, the Einstein equations generate a unique curve in conformal superspace.
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TL;DR: In this article, a Formula-based program is used to efficiently expand in components purespinor superfield expressions of kinematic factors, which can be used to obtain superstring effective actions from scattering amplitudes computed with the pure spinor formalism.
Abstract: A FORM program which is used to efficiently expand in components purespinor superfield expressions of kinematic factors is presented and comments on how it works are made. It is highly customizable using the standard features of FORM and can be used to help obtaining superstring effective actions from the scattering amplitudes computed with the pure spinor formalism.
TL;DR: In this paper, the authors studied the string instanton wrapping a non-trivial two-cycle in CP 3 of the type IIA string theory compactified on AdS 4 × CP 3 superspace and found that it has twelve fermionic zero modes associated with 1/2 of the background.
Abstract: We study the string instanton wrapping a non-trivial two-cycle in CP
3 of the type IIA string theory compactified on AdS
4 × CP
3 superspace and find that it has twelve fermionic zero modes associated with 1/2 of the supersymmetry of the background thus manifesting that this classical instanton configuration is 1/2 BPS.
TL;DR: In this article, the p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergrav-ity.
Abstract: We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergrav- ity. In particular the ten-forms, also known as "top-forms", require a careful analysis since in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear supersymmetry algebra can be introduced. We give a superspace explanation of our work. All of our results are precisely in line with the predictions of the E11 algebra.
TL;DR: In this paper, a simple BRST-closed expression for the color-ordered super-Yang-Mills 5-point amplitude at tree-level is proposed in pure spinor superspace and shown to be BRST equivalent to the field theory limit of the open superstring 5-pt amplitude.
Abstract: A simple BRST-closed expression for the color-ordered super-Yang-Mills 5-point amplitude at tree-level is proposed in pure spinor superspace and shown to be BRST-equivalent to the field theory limit of the open superstring 5-pt amplitude. It is manifestly cyclic invariant and each one of its five terms can be associated to the five Feynman diagrams which use only cubic vertices. Its form also suggests an empirical method to find superspace expressions in the cohomology of the pure spinor BRST operator for higher-point amplitudes based on their kinematic pole structure. Using this method, Ansatze for the 6- and 7-point 10D super-Yang-Mills amplitudes which map to their 14 and 42 color-ordered diagrams are conjectured and their 6- and 7-gluon expansions are explicitly computed.
TL;DR: In this paper, the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) was derived by performing group contraction on 2D superconformal algebra.
Abstract: We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in the case of two spacetime dimensions by performing group contraction on 2d superconformal algebra. We also obtain the representations of the generators in terms of superspace coordinates. Here we find realisations of the SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and develop, in parallel to the GCA studies recently in (hepth/0912.1090), the representation theory based on SGCA primaries, Ward identities for their correlation functions and their descendants which are null states.
TL;DR: In this article, the authors present a systematic analysis of the N=6 superspace constraints in three space-time dimensions, where the general coupling between vector and scalar supermultiplets is encoded in an SU(4) tensor which is a function of the matter fields and subject to a set of algebraic and superdifferential relations.
Abstract: We present a systematic analysis of the N=6 superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SU(4) tensor $W^i_j$ which is a function of the matter fields and subject to a set of algebraic and super-differential relations. We give a genuine N=6 classification for superconformal models with polynomial interactions and find the known ABJM and ABJ models. We further study the issue of supersymmetry enhancement to N=8 and the role of monopole operators in this scenario. To this end we assume the existence of a composite monopole operator superfield which we use to formulate the additional supersymmetries as internal symmetries of the N=6 superspace constraints. From the invariance conditions of these constraints we derive a system of superspace constraints for the proposed monopole operator superfield. This constraint system defines the composite monopole operator superfield analogously to the original N=6 superspace constraints defining the dynamics of the elementary fields.
TL;DR: In this paper, the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) was derived by performing group contraction on 2D superconformal algebra.
Abstract: We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in the case of two spacetime dimensions by performing group contraction on 2d superconformal algebra. We also obtain the representations of the generators in terms of superspace coordinates. Here we find realisations of the SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the representation theory based on SGCA primaries, Ward identities for their correlation functions and their descendants which are null states.
TL;DR: In this article, it was shown that CT's are not available in the real LC super-space, and the perturbative UV finiteness of d = 4 N = 8 supergravity under the assumption that supersymmetry and continuous E 7(7) symmetry are anomaly-free.
Abstract: We study counterterms (CT's), candidates for UV divergences in the four- dimensional N=8 supergravity. They have been constructed long ago in the Lorentz co- variant on shell superspace and recently in the chiral light-cone (LC) superspace. We prove that all of these CT's are ruled out since they are not available in the real LC super- space. This implies the perturbative UV finiteness of d = 4 N=8 supergravity under the assumption that supersymmetry and continuous E 7(7) symmetry are anomaly-free. The proof, based on the chiral nature of CT's in the LC superspace, is a generalization of the perturbative F-term non-renormalization theorem for N=8 supergravity.