Showing papers on "Superspace published in 1995"
Book•
23 Feb 1995TL;DR: In this paper, the Poincar-D'e group, the Lorentz group and the supergroup of general coordinate transformations on R^Tp/q were studied.
Abstract: Preface. Mathematical background: The Poincar^D'e group, the Lorentz group Finite-dimensional representations of ^ISpin(3,1) The Lorentz algebra Two-component and four-component spinors Representations of the Poincar^D'e group Elements of differential geometry and gravity The conformal group The mass-shell field representation Elements of algebra with supernumbers Elements of analysis with supernumbers The supergroup of general coordinate transformations on R^Tp/q. Supersymmetry and superspace: Introduction: from R^Tp/q to supersymmetry Superalgebras, Grassmann-shells and super Lie groups The Poincar^D'e superalgebra Unitary representation of the Poincar^D'e superalgebra Real superspace R^T4/4 and superfields Complex superspace C^T4/2, chiral superfields and covariant derivatives The on-shell massive superfield representations The on-shell massless superfield representations From superfields to component fields The superconformal group. Field theory in superspace: Supersymmetric field theory Wess-Zumino model Supersymmetric nonlinear sigma-models Vector multiplet models Supersymmetric Yang-Mills theories Geometric approach to super Yang-Mills theories Classically equivalent theories. Quantized superfields: Picture-change operators Equivalence of component field and superfield perturbation theories Effective action (super) funtional The Wess-Zumino model: perturbative analysis Note about gauge theories Feynman rules for super Yang-Mills theories Renormalization Examples of counterterm calculations: an alternative technique Superfield effective potential. Superspace geometry of supergravity: Gauge group of supergravity and supergravity fields Superspace differential geometry Supergeometry with conformal supergravity constraints Prepotentials Einstein supergravity Prepotential de formations Supercurrent and supertrace Supergravity in components. Dynamics in supergravity: Pure supergravity dynamics Linearized supergravity Superg
640 citations
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TL;DR: A survey of superspaces associated with four-dimensional Minkowski spacetime is given from a superconformal perspective in this article, which is closely related to twistor theory; in particular, the twistorial notion of a double fibration which links together sets of three such homogeneous supermanifolds is exploited to give a geometrical interpretation of super-formal transformations and is also applied to supersymmetric Yang-Mills theories.
Abstract: A survey of superspaces associated with four-dimensional Minkowski spacetime is given from a superconformal perspective. The discussion begins in the complex setting and focuses on a class of supermanifolds---flag supermanifolds---which includes not only conventional superspaces and chiral superspaces, but also supertwistor spaces and harmonic superspaces. All of them are homogeneous spaces of superconformal groups. The approach is closely related to twistor theory; in particular, the twistorial notion of a double fibration which links together sets of three such homogeneous supermanifolds is exploited to give a geometrical interpretation of superconformal transformations and is also applied to supersymmetric Yang--Mills theories. In the real setting the complex twistor space associated to Euclidean space is replaced in the supersymmetric case by supermanifolds which have a CR-structure. Representations of superconformal groups on fields are also studied; in the case of harmonic superspace this involves representations which differ slightly from standard induced representations.
185 citations
TL;DR: In this article, a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor-like formulation of super p -branes is presented.
178 citations
TL;DR: The Chern-Simons invariant of the Ashtekar-sen connection is the natural internal time coordinate for classical and quantum cosmology as discussed by the authors, which is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom.
101 citations
TL;DR: In this paper, the twistor-like superfield approach to describing super-p -branes was revised by using the basic principles of the group-manifold approach.
96 citations
TL;DR: In this article, it was shown that the space orthogonal to the kernel of the commutator of the left and right complex structures is always integrable, and hence the kernel is parametrized by chiral and twisted chiral superfield coordinates.
92 citations
TL;DR: In this article, a polynomial generalization of supersymmetry in quantum mechanics in one and two dimensions is proposed, and a detailed analysis is made for supercharges of second order with respect to derivatives.
Abstract: A polynomial generalization of supersymmetry in quantum mechanics in one and two dimensions is proposed. Polynomial superalgebras in one dimension are classified. In two dimensions, a detailed analysis is made for supercharges of second order with respect to derivatives and it is shown that in all cases the binomial superalgebra leads to hidden dynamical symmetry generated by the central charge.
89 citations
TL;DR: In this paper, a vector-like field is introduced into the supersymmetric model and the Witten index vanishes when the mass of the field is small but finite, and it decouples from the dynamics and the models reduce to the original non-calculable models.
61 citations
TL;DR: The superconformal Ward identities for Green's functions of gauge invariant operators of these types are derived in this article, and it is shown that there are no chiral super-formal invariants.
Abstract: The multiplets that occur in four dimensional rigidly supersymmetric theories can be described either by chiral superfields in Minkowski superspace or analytic superfields in harmonic superspace. The superconformal Ward identities for Green's functions of gauge invariant operators of these types are derived. It is shown that there are no chiral superconformal invariants. It is further shown that the Green's functions of analytic operators are severely restricted by the superconformal Ward when analyticity is taken into account.
57 citations
TL;DR: Self-dual supersymmetric theories are reformulated directly in conformal chiral superspace, where superconformal invariance is manifest and all the parameters are represented as a single, irreducible, constant tensor.
Abstract: We reformulate self-dual supersymmetric theories directly in conformal chiral superspace, where superconformal invariance is manifest. The superspace can be interpreted as the generalization of the usual Atiyah-Drinfel`d-Hitchin-Manin (ADHM) twistors (the quaternionic projective line), the real projective light cone in six dimensions, or harmonic superspace, but can be reduced immediately to four-dimensional chiral superspace. As an exsample, we give the `t Hooft and ADHM multi-instanton constructions for self-dual super Yang-Mills theory. In both cases, all the parameters are represented as a single, irreducible, constant tensor.
45 citations
CERN1
TL;DR: In this paper, the possible breaking of space-time supersymmetry under T-duality transformations is analyzed in detail, and it is shown that when appropriate world-sheet effects are taken into account apparent puzzles concerning supersymmymmetry in space time are solved.
TL;DR: In this paper, the full superspace measure for chiral superspace was derived, and explicit expressions for going from superspace actions to component actions were derived for both the minimal UA(1) and the extended U V (1) ⋇ U A (1).
TL;DR: In this article, it was shown that the BV (Batalin-Vilkovisky) action is invariant under a generalized anti-BRST transformation (where the antifields are the parameters of the transformation) when the gauge fixing lagrangian is both BRST and anti-brst invariant.
TL;DR: In this paper, a complete solution to the constraints for two-dimensional N = 2 supergravity in superspace was presented, and explicit expressions for the covariant derivatives in terms of the vector superfield Hm and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield ϕ.
Abstract: We present a complete solution to the constraints for two-dimensional N = 2 supergravity in N = 2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield Hm and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield ϕ.
TL;DR: A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schrodinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back reaction of the matter field.
Abstract: A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"odinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of ${\mathit{m}}_{\mathit{P}}^{2}$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.
TL;DR: In this article, two-dimensional N = 2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity were studied. And they were shown to be equivalent to the following:
Abstract: We study two-dimensional N=2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity.
01 Jan 1995
TL;DR: In this article, a covariantizing duality symmetric action is proposed, which admits a manifestly supersymmetric generalization for describing chiral superfields in n=(1, 0) D = 2 superspace.
Abstract: A way of covariantizing duality symmetric actions is proposed. As examples considered are a manifestly space-time invariant duality--symmetric action for abelian gauge fields coupled to axion-dilaton fields and gravity in D=4, and a Lorentz-invariant action for chiral bosons in D=2. The latter is shown to admit a manifestly supersymmetric generalization for describing chiral superfields in n=(1,0) D=2 superspace.
TL;DR: In this paper, the invariant integrals for chiral superspace were constructed in the framework of the prepotential description of superspace two-dimensional supergravity, and explicit expressions for going from superspace actions to component actions were given.
Abstract: In the framework of the prepotential description of superspace two-dimensional $(2,2)$ supergravity, we discuss the construction of invariant integrals. In addition to the full superspace measure, we derive the measure for chiral superspace, and obtain the explicit expressions for going from superspace actions to component actions. We consider both the minimal $U_A(1)$ and the extended $U_V(1) \otimes U_A(1)$ theories.
TL;DR: In this paper, a superspace representation of the exotic symmetry generated by spin s = 1/k and -1/k was constructed using the D=2 supersymmetric superalgebra.
Abstract: Using the D=2 (1/k,1/k) superalgebra (i.e. the two-dimensional generalized supersymmetry generated by spin s=1/k and -1/k; , charge operators Q and satisfying among other conditions and where P and are the light components of the energy--momentum operator), we build a superspace representation of this exotic symmetry. This realization generalizing the usual D=2 (1/2,1/2) supersymmetric one is based on the use of parafermionic variables and of spin s=-1/k and 1/k obeying as well as generalized commutation relation rules. Two-dimensional (1/3,0) and (1/3,1/3) invariant scalar superfield models extending the well-known D=2 (1/2,0) and (1/2,1/2) supersymmetric models are given. The link between this exotic symmetry and the periodic representation of with is worked out. Other features are also discussed.
TL;DR: In this article, Lagrangian quantization of the free superfield gauge theories of higher massless superspins is performed both in anti-de Sitter and flat superspaces.
TL;DR: In this paper, various conventional tests of integrability are applied to the supersymmetric nonlinear Schrodinger equation, and it is found that a matrix Lax pair exists and that the system has the Painleve property only for a particular choice of the free parameters of the theory.
Abstract: In this paper various conventional tests of integrability are applied to the supersymmetric nonlinear Schrodinger equation. It is found that a matrix Lax pair exists and that the system has the Painleve property only for a particular choice of the free parameters of the theory. It is also shown that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. It has not been possible to construct a zero curvature formulation of the equations based on OSp(2‖1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schrodinger equation which appears to possess the Painleve property.
TL;DR: In this paper, the uniformisation problem underlying the geometry of Wn-gravity using the differential equation approach to W-algebras is formulated using isomonodromic deformations of linear differential equations, and the Wnmanifold is obtained by the quotient of a Fuchsian subgroup of PSL(n, R ) which acts properly discontinuously on a simply connected domain in C Pn − 1.
TL;DR: In this paper, the structure of on-shell and off-shell 2D, (4,4) supersymmetric scalar multiplets is investigated, in components and in superspace.
Abstract: The structure of on-shell and off-shell 2D, (4,4) supersymmetric scalar multiplets is investigated, in components and in superspace. We reach the surprising result that there exist eight {\underline {distinct}} on-shell versions and an even greater variety of off-shell ones. The off-shell generalised tensor and relaxed N = 4 multiplets are introduced in superspace, and their universal invariant self-interaction is constructed.
TL;DR: In this article, the super-Pauli-Ljubanski vector of an odd Grassmann character is described as a super-Poincare algebra, which generates spinors.
Abstract: In this theory scalars, spinors, and vectors are described as particles living in a d‐dimensional ordinary and a d‐dimensional Grassmann space, with d≥5. Operators of translations and the Lorentz transformations in both spaces form the super‐Poincare algebra. It is the super‐Pauli–Ljubanski vector of an odd Grassmann character, which generates spinors. The theory offers a new insight into quantum theory of particles and their supersymmetric nature.
Posted Content•
TL;DR: In this article, a covariantizing duality symmetric action is proposed, which admits a manifestly supersymmetric generalization for describing chiral superfields in n=(1, 0) D = 2 superspace.
Abstract: A way of covariantizing duality symmetric actions is proposed. As examples considered are a manifestly space-time invariant duality--symmetric action for abelian gauge fields coupled to axion-dilaton fields and gravity in D=4, and a Lorentz-invariant action for chiral bosons in D=2. The latter is shown to admit a manifestly supersymmetric generalization for describing chiral superfields in n=(1,0) D=2 superspace.
TL;DR: In this article, a supersymmetric superparticle action is constructed using geometrical objects that characterize the embedding of the worldline superspace into the target superspace.
Abstract: We consider a formulation of N=1, D=3, 4 and 6 superparticle mechanics, which is manifestly supersymmetric on the worldline and in the target superspace For the construction of the action we use only geometrical objects that characterize the embedding of the worldline superspace into the target superspace, such as target superspace coordinates of the superparticle and twistor components The action does not contain the Lagrange multipliers which may cause the problem of infinite reducible symmetries, and, in fact, is a worldline superfield generalization of the supertwistor description of superparticle dynamics
TL;DR: In this article, a reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying generalised Cauchy-Riemann conditions.
TL;DR: In this article, a functional approach of euclidean quantum field theory is formulated for supersymmetry, and the relation of the euclidesymmetric Lie superalgebra and its relation to the Poincare Lie super algebra is investigated.
Abstract: Supersymmetry is formulated within a functional approach of euclidean quantum field theory. The rǒle of the euclidean Lie superalgebra and its relation to the Poincare Lie superalgebra are investigated in detail. As example we study the Wess-Zumino model in two dimensions.
TL;DR: It is proved that a reasonable definition of the gravitational binding energy is always negative, and a one-parameter family of linear extrinsic time foliations of spacetime is introduced.
Abstract: We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter variables, there exist two linear combinations of the Hamiltonian and momentum constraints which are related by time reversal. We introduce a one-parameter family of linear extrinsic time foliations of spacetime. The values of the parameter yielding globally valid gauges correspond to the vanishing of a timelike vector in the superspace of spherically symmetric geometries. We define a quasi-local mass on spheres of fixed proper radius which we prove is positive when the constraints are satisfied. Underpinning the proof are various local bounds on the configuration variables. We prove that a reasonable definition of the gravitational binding energy is always negative. Finally, we provide a tentative characterization of the configuration space of the theory in terms of closed bounded trajectories on the parameter space of the optical scalars.
TL;DR: In this article, the kappa-deformed D = 4 Poincare superalgebra is transformed to the basis with classical Lorentz subalgebra generators, and it is shown that in such a basis, the KDE can be written as a graded bicrossproduct.
Abstract: The kappa-deformed D=4 Poincare superalgebra written in Hopf superalgebra form is transformed to the basis with classical Lorentz subalgebra generators. We show that in such a basis the kappa-deformed D=4 Poincare superalgebra can be written as a graded bicrossproduct. We show that the kappa-deformed D=4 superalgebra acts covariantly on a kappa-deformed chiral superspace.