Showing papers on "Superspace published in 2019"
TL;DR: In this paper, a supersymmetric generalization of the solvable solvable supercurrent deformation of two-dimensional field theories is proposed, where the energy levels of the resulting deformed theory are determined exactly in terms of those of the undeformed theory.
Abstract: We propose a manifestly supersymmetric generalization of the solvable $$ T\overline{T} $$
deformation of two-dimensional field theories. For theories with (1, 1) and (0, 1) supersymmetry, the deformation is defined by adding a term to the superspace Lagrangian built from a superfield containing the supercurrent. We prove that the energy levels of the resulting deformed theory are determined exactly in terms of those of the undeformed theory. This supersymmetric deformation extends to higher dimensions, where we conjecture that it might provide a higher-dimensional analogue of $$ T\overline{T} $$
, producing supersymmetric Dirac or Dirac-Born-Infeld actions in special cases.
62 citations
TL;DR: In this article, the authors extend the notion of super-Minkowski space-time to include Z 2 n -graded (Majorana) spinor coordinates, which are nilpotent but commute amongst themselves.
Abstract: We extend the notion of super-Minkowski space-time to include Z 2 n -graded (Majorana) spinor coordinates. Our choice of the grading leads to spinor coordinates that are nilpotent but commute amongst themselves. The mathematical framework we employ is the recently developed category of Z 2 n -manifolds understood as locally ringed spaces. The formalism we present resembles N -extended superspace (in the presence of central charges), but with some subtle differences due to the exotic nature of the grading employed.
35 citations
TL;DR: In this paper, the superfield representation for all cubic interaction vertices of the supermultiplets is derived, and the relativistic symmetries of N = 1 Poincare superalgebra on space of interacting superfields are also found.
Abstract: In the framework of light-cone gauge formulation, massless arbitrary spin N=1 supermultiplets in four-dimensional flat space are considered. We study both the integer spin and half-integer spin supermultiplets. For such supermultiplets, formulation in terms of unconstrained light-cone gauge superfields defined in momentum superspace is used. Superfield representation for all cubic interaction vertices of the supermultiplets is obtained. Representation of the cubic vertices in terms of component fields is derived. Realization of relativistic symmetries of N=1 Poincare superalgebra on space of interacting superfields is also found.
32 citations
TL;DR: In this article, supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued are presented. But they do not capture all the dependence on the worldsheet punctures, and the coefficient of the holomorphic Eisenstein series G4.
Abstract: In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is the generalization of a so far unnoticed property at tree-level; the correlators have the symmetry structure akin to Lie polynomials. One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties. These expressions are related via identities obeyed by the kinematic superfields and worldsheet functions spelled out in the first two parts of this series and reflecting a duality between the two kinds of ingredients. Interestingly, the expression for the eight-point correlator following from our method seems to capture correctly all the dependence on the worldsheet punctures but leaves undetermined the coefficient of the holomorphic Eisenstein series G4. By virtue of chiral splitting, closed-string correlators follow from the double copy of the open-string results.
31 citations
TL;DR: In this article, a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles is described, and a rich variety of multiparticle superfields which are local, have covariant BRST variations, and are compatible with the particularities of the pure-spinor amplitude prescription is investigated.
Abstract: This is the first installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this first part, we exploit the synergy between the co-homological features of pure-spinor superspace and the pure-spinor zero-mode integration rules of the one-loop amplitude prescription. This leads to the study of a rich variety of multiparticle superfields which are local, have covariant BRST variations, and are compatible with the particularities of the pure-spinor amplitude prescription. Several objects related to these superfields, such as their non-local counterparts and the so-called BRST pseudo-invariants, are thoroughly reviewed and put into new light. Their properties will turn out to be mysteriously connected to products of one-loop worldsheet functions in packages dubbed “generalized elliptic integrands”, whose prominence will be seen in the later parts of this series of papers.
30 citations
TL;DR: In this article, a superspace representation for all cubic interactions vertices of the N-extended massless supermultiplets was developed for the light-cone gauge superfield formulation.
Abstract: N-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build unconstrained light-cone gauge superfield formulation. The superfield formulation is used to develop a superspace representation for all cubic interactions vertices of the N-extended massless supermultiplets. Our suitable treatment of the light-cone gauge superfields allows us to obtain attractively simple superspace representation for the cubic interaction vertices. Superspace realization of relativistic symmetries of the N-extended Poincare superalgebra on space of interacting fields is also obtained.
26 citations
TL;DR: In this article, a superspace representation for all cubic interactions vertices of the massless supermultiplets was derived by using light-cone momentum superspace, and the superfield formulation was used to obtain an attractively simple superspace representation for the cubic interaction vertices.
Abstract: $$ \mathcal{N} $$
-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build unconstrained light-cone gauge superfield formulation. The superfield formulation is used to develop a superspace representation for all cubic interactions vertices of the $$ \mathcal{N} $$
-extended massless supermultiplets. Our suitable treatment of the light-cone gauge superfields allows us to obtain attractively simple superspace representation for the cubic interaction vertices. Su- perspace realization of relativistic symmetries of the $$ \mathcal{N} $$
-extended Poincare superalgebra on space of interacting fields is also obtained.
25 citations
TL;DR: In this paper, a supersymmetric continuous spin representation in 4 D, N = 1 Minkowski superspace at the level of equations of motions is proposed. But the superspace constraints for both representations generate the expected Wigner's conditions.
24 citations
TL;DR: In this paper, a supersymmetric s o (n ) spin-Calogero model with an arbitrary even number of supersymmetries was constructed, and a superspace description for the simplest case, namely N = 2 supersymmetry was provided.
24 citations
TL;DR: In this paper, the authors formulate the locally supersymmetric E7(7) exceptional field theory in a (4 + 56|32) dimensional superspace, corresponding to a 4D N = 8 "external" superspace augmented with an "internal" 56-dimensional space.
Abstract: We formulate the locally supersymmetric E7(7) exceptional field theory in a (4 + 56|32) dimensional superspace, corresponding to a 4D N = 8 “external” superspace augmented with an “internal” 56-dimensional space. This entails the unification of external diffeomorphisms and local supersymmetry transformations into superdiffeomorphisms. The solutions to the superspace Bianchi identities lead to on-shell duality equations for the p-form field strengths for p ≤ 4. The reduction to component fields provides a complete description of the on-shell supersymmetric theory. As an application of our results, we perform a generalized Scherk-Schwarz reduction and obtain the superspace formulation of maximal gauged supergravity in four dimensions parametrized by an embedding tensor.
22 citations
TL;DR: In this article, a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism is introduced, which enables the authors to construct massive onshell superfields and fully utilize onshell symmetry considerations to derive all possible three-particle amplitudes for particles of spin as high as one.
Abstract: We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible $$ \mathcal{N} $$
= 1 three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.
TL;DR: In this article, a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional was proposed, which allows to define an entropy current quantum mechanically by coupling it to an external source.
Abstract: We provide a mechanism by which an entropy current can be constructed in a supersymmetric formulation of the low-energy effective action for the Schwinger-Keldysh generating functional. This mechanism allows us to define an entropy current quantum mechanically by coupling it to an external source. Such an entropy current is given by the bottom component of an entropy current superfield which is conserved in superspace, but when restricted to real space satisfies a non-conservation law. We demonstrate the validity of our mechanism in a probe limit which allows us to fully treat quantum fluctuations.
TL;DR: In this paper, the authors describe the supersymmetric completion of several curvature-squared invariants for (1, 0) supergravity in six dimensions, based on a close interplay between superconformal tensor calculus and recently developed superspace techniques.
Abstract: We describe the supersymmetric completion of several curvature-squared invariants for $$ \mathcal{N} $$
= (1, 0) supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincare supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet super-gravity, which plays a central role in the effective low-energy description of α′-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the AdS3 × S3 solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS6 solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvaturesquared terms and possesses a nontrivial dependence on the dilaton field.
TL;DR: In this paper, a supersymmetric theory with F-term couplings in 2 + 1 dimensions, obtained by null reduction of a relativistic Wess-Zumino model, was considered and the causal structure of the nonrelativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
Abstract: We consider a Galilean $$ \mathcal{N}=2 $$
supersymmetric theory with F-term couplings in 2 + 1 dimensions, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
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TL;DR: In this article, a review about the Minimal Supersymmetric Standard Model (MSSM) and the General Singlet Extensions of the MSSM (GSEMSSM).
Abstract: In this lectures, we give a review about the Minimal Supersymmetric Standard Model (MSSM) and the General Singlet Extensions of the MSSM (GSEMSSM). We, first introduce the minimal set of fields to built both models. Then we introduce their superfields and using them we build the lagrangian of those models in the superspace formalism. We show how to get the mass spectrum of those model in the $R$-parity scenarios and we also show how to get some Feynman Rules with the Gauge Bosons.
TL;DR: In this paper, the off-shell actions were recast in terms of unconstrained gauge prepotentials as integrals over the full superspace, and they were derived transverse projection operators in the Minkowski superspace and then used to construct linearised rank n super-Cotton tensors.
Abstract: The off-shell actions for $$ \mathcal{N} $$
-extended conformal supergravity theories in three dimensions were formulated in [1, 2] for 1 ≤ $$ \mathcal{N} $$
≤ 6 using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $$ \mathcal{N} $$
-extended conformal superspace. In this paper we initiate a program to recast these actions (and to formulate their higher-spin counterparts) in terms of unconstrained gauge prepotentials as integrals over the full superspace. We derive transverse projection operators in $$ \mathcal{N} $$
-extended Minkowski superspace and then use them to construct linearised rank-n super-Cotton tensors and off-shell $$ \mathcal{N} $$
-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin super-multiplets in $$ \mathcal{N} $$
-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $$ \mathcal{N} $$
-extended supersymmetry.
TL;DR: In this paper, the authors consider conformal and 't Hooft anomalies in six-dimensional superconformal field theories, focusing on those conformal anomalies that determine the two-and three-point functions of conserved flavor and $SU(2)_R$ currents, as well as stress tensors.
Abstract: We consider conformal and 't Hooft anomalies in six-dimensional ${\cal N}=(1,0)$ superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and $SU(2)_R$ currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non-supersymmetric CFTs in six dimensions have three independent conformal $c$-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three $c$-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its 't Hooft anomalies. Following earlier work on the conformal $a$-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.
TL;DR: In this article, the superfield representation for all cubic interaction vertices of the supermultiplets is derived in terms of component fields, and the relativistic symmetries of N = 1 Poincare superalgebra on space of interacting superfields is also found.
Abstract: In the framework of light-cone gauge formulation, massless arbitrary spin N=1 supermultiplets in four-dimensional flat space are considered. We study both the integer (super)spin and half-integer (super)spin supermultiplets. For such supermultiplets, formulation in terms of unconstrained light-cone gauge superfields defined on chiral momentum superspace is used. Superfield representation for all cubic interaction vertices of the supermultiplets is obtained. Representation of the cubic vertices in terms of component fields is derived. Realization of relativistic symmetries of N=1 Poincare superalgebra on space of interacting superfields is also found.
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TL;DR: In this article, the authors studied the holomorphic twist of four-dimensional superconformal algebras, and showed that the resulting higher symmetry algebra acts naturally by holomorphic vector fields on holomorphically twisted superformal theories.
Abstract: We compute the holomorphic twists of four-dimensional superconformal algebras, and argue that the resulting algebras act naturally by holomorphic vector fields on holomorphically twisted superconformal theories. We demonstrate that this symmetry enhances to the action of an infinite-dimensional local Lie algebra, the Dolbeault resolution of all holomorphic vector fields on a punctured superspace. Global symmetries also enhance to the Dolbeault resolution of holomorphic functions valued in the Lie algebra; at the classical level, both of these higher symmetry algebras act naturally on the holomorphic twist of any Lagrangian theory, whether superconformal or not. We show that these algebras are related to two-dimensional chiral algebras extracted from four-dimensional superconformal theories in recent work; further deforming the differential induces the Koszul resolution of a plane in $\mathbb{C}^2$, and the cohomology of the higher symmetry algebras are the usual Virasoro and Kac-Moody chiral algebras. We show that the central extensions of those chiral algebras arise from recently studied central extensions of our higher symmetry algebras. However, the higher algebras admit many further deformations not originating in the global superconformal algebra; these localize to any smooth complex curve in $\mathbb{C}^2$, resolving the holomorphic vector fields there, and expect that they will lead to even more exotic behavior in the case of singular or nonreduced curves. We consider explicit examples of $\mathcal{N}=2$ gauge theories, and demonstrate that an anomaly to realizing the higher symmetry algebra at the quantum level vanishes precisely when the theory is, in fact, superconformal; for such theories, we also give an explicit description of the chiral algebras that result after further deformation.
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TL;DR: In this article, the off-shell actions for higher-spin supergravity theories were formulated in terms of unconstrained gauge prepotentials as integrals over the full superspace.
Abstract: The off-shell actions for $\cal N$-extended conformal supergravity theories in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using a universal approach. Each action is generated by a closed super three-form which is constructed in terms of the constrained geometry of $\cal N$-extended conformal superspace. In this paper we initiate a program to recast these actions (and to formulate their higher-spin counterparts) in terms of unconstrained gauge prepotentials as integrals over the full superspace. We derive transverse projection operators in $\cal N$-extended Minkowski superspace and then use them to construct linearised rank-$n$ super-Cotton tensors and off-shell $\cal N$-extended superconformal actions. We also propose off-shell gauge-invariant actions to describe massive higher-spin supermultiplets in $\cal N$-extended supersymmetry. Our analysis leads to general expressions for identically conserved higher-spin current multiplets in $\cal N$-extended supersymmetry.
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TL;DR: In this paper, the authors present a series of lecture notes from the Winter School "YRISW 2018" to appear in a special issue of JPhysA. Their intention is to understand how much we can learn from representation theory alone, even about the dynamics of 4D $\mathcal{N}=2$ SCFTs.
Abstract: This is the writeup of the lectures given at the Winter School "YRISW 2018" to appear in a special issue of JPhysA. In the first part of these lecture notes we review some important facts about 4D $\mathcal{N}=2$ SCFTs. We begin with basic textbook material, the supersymmetry algebra and its massless representations and the construction of Lagrangians using superspace. Then we turn to more modern topics, the study of the $\mathcal{N}=2$ SCA and its representation theory. Our intention is to understand how much we can learn from representation theory alone, even about the dynamics of $\mathcal{N}=2$ SCFTs. In the second part of the notes we use these tools to construct spin chains for $\mathcal{N}=2$ SCFTs, the spectral problem of which computes anomalous dimensions of local operators. We discuss their novel features comparing them with their counterparts in $\mathcal{N}=4$ SYM and search for possible integrability structures that emerge.
TL;DR: In this paper, the authors present a systematic method to expand in components four dimensional superconformal multiplets and prove that certain chiral operators do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT.
Abstract: We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible $\mathcal{N} = 1$ multiplets and some cases of interest for $\mathcal{N} = 2$. As an application of the formalism we prove that certain $\mathcal{N} = 2$ spinning chiral operators (also known as "exotic" chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of three-point functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace.
TL;DR: In this paper, the authors provided the explicit form of the action for the mass-deformed supersymmetric Chern-Simons-matter theory, which admits a unique triplet mass deformation term consistent with supersymmetry.
Abstract: The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N}=3$ supersymmetry. In this short paper, we provide the explicit form of the action for the mass-deformed $\mathcal{N}=3$ supersymmetric $U(N)$ Chern-Simons-matter theory. The theory admits a unique triplet mass-deformation term consistent with supersymmetry. We explicitly construct the mass-deformed $\mathcal{N}=3$ theory in $\mathcal{N}=1$ superspace using a fundamental and an antifundamental superfield.
TL;DR: A brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics, based on the worldline realizations of the supergroups SU( 2|2) and SU(4|1), in the appropriate N =8, d = 1 superspaces.
Abstract: We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m.
TL;DR: In this article, the class of conservative superalgebras, in particular, the superalgebra U(V) of bilinear operations on a superspace V, is introduced.
Abstract: We introduce the class of conservative superalgebras, in particular, the superalgebra U(V) of bilinear operations on a superspace V. Moreover, we show that each conservative superalgebra modulo its...
TL;DR: In this article, a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism is introduced, which enables them to construct massive on-hell superfields and fully utilize on- shell symmetry considerations to derive all possible three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes of any spin.
Abstract: We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible $\mathcal{N}=1$ three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.
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TL;DR: In this article, a superspace Vandermonde determinant is extended to superspace of rank $n, and a notion of partial differentiation with respect to anticommuting variables is defined to construct doubly graded modules.
Abstract: Superspace of rank $n$ is a $\mathbb{Q}$-algebra with $n$ commuting generators $x_1, \dots, x_n$ and $n$ anticommuting generators $\theta_1, \dots, \theta_n$. We present an extension of the Vandermonde determinant to superspace which depends on a sequence $\mathbf{a} = (a_1, \dots, a_r)$ of nonnegative integers of length $r \leq n$. We use superspace Vandermondes to construct graded representations of the symmetric group. This construction recovers hook-shaped Tanisaki quotients, the coinvariant ring for the Delta Conjecture constructed by Haglund, Rhoades, and Shimozono, and a superspace quotient related to positroids and Chern plethysm constructed by Billey, Rhoades, and Tewari. We define a notion of partial differentiation with respect to anticommuting variables to construct doubly graded modules from superspace Vandermondes. These doubly graded modules carry a natural ring structure which satisfies a 2-dimensional version of Poincare duality. The application of polarization operators gives rise to other bigraded modules which give a conjectural module for the symmetric function $\Delta'_{e_{k-1}} e_n$ appearing in the Delta Conjecture of Haglund, Remmel, and Wilson.
TL;DR: In this paper, the authors introduce (conformal) Killing tensor superfields with non-negative integers, and elaborate on their significance in the context of supersymmetric field theory in curved space.
Abstract: In four spacetime dimensions, all ${\cal N} =1$ supergravity-matter systems can be formulated in the so-called $\mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $\mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields $\ell_{(\alpha_1 \dots \alpha_m) ({\dot \alpha}_1 \dots {\dot \alpha}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields $\ell_{\alpha \dot \alpha}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields $\ell_{\alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.
TL;DR: In this paper, the authors revisited the formalism of 110 polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 110 ambitwistor superstring action.
Abstract: We revisited the formalism of 110 polarized scattering equation by Geyer and Mason from the perspective of spinor frame approach and spinor moving frame formulation of the 110 ambitwistor superstring action. In particular, we rigorously obtain the equation for the spinor function on Riemann sphere from the supertwistor form of the ambitwistor superstring action, write its general solution and use it to derive the polarized scattering equation. We show that the expression used by Geyer and Mason to motivate their ansatz for the solution of polarized scattering equation can be obtained from our solution after a suitable gauge fixing. To this end we use the hidden gauge symmetries of the 110 ambitwistor superstring, including S0(16), and the description of ambitwistor superstring as a dynamical system in an 110 superspace enlarged by bosonic directions parametrized by 517 tensorial central charge coordinates $$ {Z}^{\underline{\mu}\underline {
u }} $$
and $$ {Z}^{\underline{\mu}\underline {
u}\underline{\rho}\underline {\sigma}\underline{\kappa}} $$
. We have also found the fermionic superpartner of the polarized scattering equation. This happens to be a differential equation in fermionic variables imposed on the super amplitude, rather then just a condition on the scattering data as the bosonic polarized scattering equation is. D=10 case is also discussed stressing the similarities and differences with 110 systems. The useful formulation of 100 ambitwistor superstring considers it as a dynamical system in superspace enlarged with 126 tensorial central charge coordinates Zμνρσκ.
TL;DR: In this article, a superspace version of the Stuckelberg procedure is formulated, which restores diffeomorphism and local supersymmetry invariance without the need of introducing any matter.
Abstract: Understanding de Sitter space in supergravity - and string theory - has lead to an intense amount of work for more than two decades, largely motivated by the discovery of the accelerated expansion of the universe in 1998. In this paper, we consider a non-trivial generalisation of unimodular gravity to minimal N = 1 supergravity, which allows for de Sitter solutions without the need of introducing any matter. We formulate a superspace version of the Stuckelberg procedure, which restores diffeomorphism and local supersymmetry invariance. This introduces the goldstino associated to spontaneous breaking of supersymmetry in a natural way. The cosmological constant and gravitino mass are related to the vacuum expectation value of the components of a Lagrange multiplier imposing a super-unimodularity condition.