Lars Brink, Sung-Soo Kim, Pierre Ramond
We derive the non-linear action of E8(8) on the constrained chiral superfield in the light-cone superspace with eight complex Grassmann variables. We construct (to lowest order in the coupling) the sixteen dynamical supersymmetries which generate a Hamiltonian with E8(8) invariance in three space-time dimensions, and show that it has only interactions with even powers of the coupling constant.
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We find a manifestly N=3 supersymmetric generalization of the four-dimensional Euler-Heisenberg (four-derivative, or F^4) part of the Born-Infeld action in light-cone gauge, by using N=3 light-cone superspace.
The BPS bound is formulated in light-cone superspace for the N = 4 superYang-Mills theory. As a consequence of the superalgebra all momenta are shown to be expressed as a quadratic form in the relevant supertransformations, and these forms are used to derive the light-cone superspace BPS equations. Finally, the superfield expressions are expanded out to component form, and the Wu-Yang Monopole boosted to the infinite momentum frame is shown to be a solution.
The recently formulated Bagger-Lambert-Gustavsson (BLG) theory in three dimensions is described in terms of a constrained chiral superfield in light-cone superspace. We discuss the use of Superconformal symmetry to determine the form of its interactions, in complete analogy with N=4 SuperYang-Mills in four dimensions.
The light-cone superspace version of the d=3, N=8 superconformal theory of Bagger, Lambert and Gustavsson (BLG) is obtained as a solution to constraints imposed by OSp(2,2|8) superalgebra. The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformation.
We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.
We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant κ, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured.
We initiate a study of correlation functions of gauge-invariant operators in N=4 super Yang-Mills theory using the light-cone superspace formalism. Our primary aim is to develop efficient methods to compute perturbative corrections to correlation functions. This analysis also allows us to examine potential subtleties which may arise when calculating off-shell quantities in light-cone gauge. We comment on the intriguing possibility that the manifest N=4 supersymmetry in this approach may allow for a compact description of entire multiplets and their correlation functions.
Exceptional symmetries in light-cone superspace
本文通过氧化四维N=8超引力构造五维最大超引力，在光锥超空间中展示USp(8)与E6对称性及其与SU(8)、E7的联系，并利用例外对称性推导出四、五次相互作用顶点。
Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a {non-central} extension of the d=3 N=8 Poincare superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being {cubic} in the kinematical ones. The mass deformation picks a quaternionic direction, which breaks the SO(8) R-symmetry down to SO(4)xSO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations, to all orders in the mass para…
Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell N=2 supersymmetric sigma model, with the target space corresponding to a generic 4n-dimensional hyperkahler cone. We show how the component action coupling the hypermultiplets to conformal supergravity may be constructed starting from curved superspace. The superspace origin of the geometric data -- th…
Light-cone vector superspace and continuous-spin field in AdS
本文在光锥 gauge 向量超空间框架下研究AdS空间中连续自旋场，提出连续自旋场的分类并探讨其无质量性质，同时获得四维AdS非线性自旋代数的所有单元性不可约表示。
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 ve…
Interacting massive/massless continuous-spin fields and integer-spin fields
本文在光锥协言框架下研究了重/无质量连续自旋场与整数自旋场的相互作用，推导了相关三重顶点并展示了公式的等价性。
We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse direct…
We analyze the superfield constraints of the D=4, N=3 SYM-theory using light-cone gauge conditions. The SU(3)/U(1)xU(1) harmonic variables are interpreted as auxiliary spectral parameters, and the transform to the harmonic-superspace representation is considered. Our nilpotent gauge for the basic harmonic superfield simplifies the SYM-equations of motion. A partial Grassmann decomposition of these equations yields the solvable linear system of iterative equations.
We analyze the superfield equations of the 4-dimensional N=4 SYM-theory using light-cone gauge conditions and the harmonic-superspace approach. The harmonic superfield equations of motion are drastically simplified in this gauge, in particular, the basic harmonic-superfield matrices and the corresponding harmonic analytic gauge connections become nilpotent on-shell.
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 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 example, 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,…
We analyze the superfield constraints of the D=4, N=3 SYM-theory using light-cone gauge conditions. The SU(3)/U(1) x U(1) harmonic variables are interpreted as auxiliary spectral parameters, and the transform to the harmonic-superspace representation is considered. The harmonic superfield equations of motion are drastically simplified in our gauge, in particular, the basic matrix of the harmonic transform and the corresponding harmonic analytic gauge connections become nilpotent on-shell. It is shown that these harmonic SYM-equations are equivalent to the finite set of solvable linear iterativ…
Maximally supersymmetric theories can be described by a single scalar superfield in light-cone superspace. When they are also (super)conformally invariant, they are uniquely specified by the form of the dynamical supersymmetry. We present an explicit derivation of the light-cone superspace form of the dynamical supersymmetry in the cases of ten- and four-dimensional super-Yang-Mills, and the three-dimensional Bagger-Lambert-Gustavsson theory, starting from the covariant formulation of these theories.
The Lorentz covariant all-loop counterterms built in the 4+32 on shell superspace of N=8 supergravity imply that the theory is not UV finite. Meanwhile, the relevant counterterms depending on the light-cone superfields in 4+16 superspace have not been constructed so far. Our first attempt to construct them suggests that they may be incompatible with the covariant ones. This would lead to a prediction of all-loop UV finiteness of the perturbative S-matrix. Here we rely on the validity of the equivalence theorem for the S-matrix in the light-cone gauge and Lorentz covariant gauges, which require…
The N-extended self-dual supergravity in the ultra-hyperbolic four-dimensional spacetime of kleinian signature (2+2) is given in the N-extended harmonic superspace. We reformulate the on-shell N-extended self-dual supergravity constraints of Siegel to a `zero-curvature' representation, and solve all of them but one in terms of a single superfield prepotential, by using a covariant Frobenius gauge in the Devchand-Ogievetsky approach. An off-shell superspace action, whose equation of motion yields the remaining constraint, is found. Our manifestly Lorentz-covariant action in harmonic superspace …
We analyze the superfield equations of the 4-dimensional N=2 and N=4 SYM-theories using light-cone gauge conditions and the harmonic-superspace approach. The harmonic superfield equations of motion are drastically simplified in this gauge, in particular, the basic harmonic-superfield matrices and the corresponding harmonic analytic gauge connections become nilpotent on-shell.
Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N=2 Poincare superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generator…
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q<=4 (for N>4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be supercon…
Superspace Expansion of The 11D Linearized Superfields in The Pure Spinor Formalism, and The Covariant Vertex Operator
本文利用类Harnad-Shnider规范中的递归关系求得线性化11维超引力超场的θ全阶超空间展开，并借助11维 ABC 超粒子首次构造完全协变顶点算子，且证明其在光锥规范下重现GGK算子。
We describe various aspects of two-dimensional $N=2$ supergravity in superspace. We present the solution to the constraints in terms of unconstrained prepotentials, and the different superspace measures (full and chiral) used in the construction of invariant actions. We discuss aspects of the theory in light-cone gauge, including the Ward identities for correlation functions defined with respect to the induced supergravity action.
We introduce a new set of effective field theory rules for constructing Lagrangians with $\mathcal{N} = 1$ supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $(x^μ,θ^α, θ^{\dagger \dotα})$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary $F$- and $D$-term components. By contrast, collinear superspace depends on a smaller set of coordinates $(x^μ,η,η^\dagger)$, where $η$ is a complex Grassmann number without a spinor index. This provides a formulation of supersymme…
Soft factors and interaction vertices from light-cone actions
本文在光锥规范下提出软玻色子发射的普适因子，回顾逆软方法，并应用于N=4超杨-米尔斯和N=8超引力，得到N=8超引力中四次顶点的紧凑结果，对有限性分析至关重要。
Dimensionally reduced supersymmetric theories retain a great deal of information regarding their higher dimensional origins. In superspace, this "memory" allows us to restore the action governing a reduced theory to that describing its higher-dimensional progenitor. We illustrate this by restoring four-dimensional N=4 Yang-Mills to its six-dimensional parent, N=(1,1) Yang-Mills. Supersymmetric truncation is introduced into this framework and used to obtain the N=1 action in six dimensions. We work in light-cone superspace, dealing exclusively with physical degrees of freedom.
We consider the open superstring ending on a D-brane in the presence of a constant NS-NS B field, using the Green-Schwarz formalism. Quantizing in the light-cone gauge, we find that the anti-commutation relations for the fermionic variables of superspace remain unmodified. We also derive the unbroken supersymmetry algebra living on the D-brane. This establishes how the Moyal product is extended in a superspace formulation of non-commutative field theories. The superfield formulation of non-commutative supersymmetric field theories is briefly considered.
This paper considers closed-string states of type 2b superstring theory in which the whole string is localized at a single point in superspace. Correlation functions of these (scalar and pseudoscalar) states possess an infinite number of position-space singularities inside and on the light-cone as well as a space-like singularity outside the light-cone.\foot{This paper was previously produced as preprint QMW-91-02.}
The $N=4$ supersymmetric self-dual Yang-Mills theory in a four- dimensional space with signature $(2,2)$ is formulated in harmonic superspace. The on-shell constraints of the theory are reformulated in the equivalent form of vanishing curvature conditions for three gauge connections (one harmonic and two space-time). The constraints are then obtained as variational equations from a superspace action of the Chern-Simons type. The action is manifestly $SO(2,2)$ invariant. It can be viewed as the Lorentz-covariant form of the light-cone superfield action proposed by Siegel.
We consider three-dimensional maximally superconformal Bagger-Lambert-Gustavsson (BLG) theory and its topologically gauged version (constructed recently in arXiv:0809.4478 [hep-th]) in the light-cone gauge. After eliminating the entire Chern-Simons gauge field, the ungauged BLG theory looks more conventional and, apart from the order of the interaction terms, resembles N=4 super-Yang-Mills theory in four dimensions. The light-cone superspace version of the BLG theory is given to quadratic and quartic order and some problems with constructing the sixth order interaction terms are discussed. In …
Nicolai maps and uniqueness in the light-cone gauge
本文计算了光锥规范下超对称杨-米尔斯理论在临界维度中的Nicolai映射至二阶，证明四费米子项无害，并探讨了d=4中映射的唯一性及超空间中的映射。
Light-cone gauge manifestly supersymmetric formulation of eleven dimensional supergravity is developed. The formulation is given entirely in terms of light cone scalar superfield, allowing us to treat all component fields on an equal footing. All higher derivative on mass shell manifestly supersymmetric 4-point functions invariant with respect to linear supersymmetry transformations and corresponding (in gravitational bosonic sector) to terms constructed from four Riemann tensors and derivatives are found. Superspace representation for 4-point scattering amplitudes is also obtained. Superfield…
In this paper we construct a light-like polygonal Wilson loop in N=6 superspace for ABJM theory. We then use it to obtain constraints on its two- and three-loop bosonic version, by focusing on higher order terms in the $θ$ expansion. The Grassmann expansion of the three-loop answer contains integrals which may be elliptic polylogarithms. Our results take their simplest form when expressed in terms of OSp(6|4) supertwistors.
A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules are then used to construct the supersymmetric generalization of the covariant Moyal star product in noncommutative superspace. As one of the possible applications, we propose this new product as the star product in supersymmetric string field theory. Furthermore, the formalism introduces…
We construct the covariant $κ$-symmetric superstring action for type $IIB$ superstring on plane wave space supported by Ramond-Ramond background. The action is defined as a 2d sigma-model on the coset superspace. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz superstring action and find the light-cone string Lagrangian and the Hamiltonian. The resulting light-cone gauge action is quadratic in both the bosonic and fermionic superstring 2d fields, and therefore, this model can be explicitly quantized. We also obtain a realization of the generators of the basic …
We study counterterms (CT's), candidates for UV divergences in the four-dimensional N=8 supergravity. They have been constructed long ago in a Lorentz covariant 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 superspace. This implies the perturbative UV finiteness of d=4 N=8 supergravity under the assumption that supersymmetry and continuous E7 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…
We employ the light-cone superspace formalism to develop an efficient approach to constructing superconformal operators of twist two in Yang-Mills theories with N=1,2,4 supercharges. These operators have an autonomous scale dependence to one-loop order and determine the eigenfunctions of the dilatation operator in the underlying gauge theory. We demonstrate that for arbitrary N the superconformal operators are given by remarkably simple, universal expressions involving the light-cone superfields. When written in components field, they coincide with the known results obtained by conventional te…
We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the N=4 superfield and its conjugate to a new pair of superfields. In terms of these new superfields the N=4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in …
This paper reviews the covariant formalism of N=1, D=10 classical superparticle models. It discusses the local invariances of a number of superparticle actions and highlights the problem of finding a covariant quantization scenario. Covariant quantization has proved problematic, but it has motivated in seeking alternative approaches that avoids those found in earlier models. It also shows new covariant superparticle theories formulated in extended spaces that preserve certain canonical form in phase-space, and easy to quantize by using the Batalin-Vilkovisky procedure, as the gauge algebra of …
We consider a supersymmetric Wilson loop operator for 4d N=4 super Yang-Mills theory which is the natural object dual to the AdS_5 x S^5 superstring in the AdS/CFT correspondence. It generalizes the traditional bosonic 1/2 BPS Maldacena-Wilson loop operator and completes recent constructions in the literature to smooth (non-light-like) loops in the full N=4 non-chiral superspace. This Wilson loop operator enjoys global superconformal and local kappa-symmetry of which a detailed discussion is given. Moreover, the finiteness of its vacuum expectation value is proven at leading order in perturbat…
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 super…
$D$-brane boundary states for type II superstrings are constructed by enforcing the conditions that preserve half of the space-time supersymmetry. A light-cone coordinate frame is used where time is identified as one of the coordinates transverse to the brane's (euclidean) world-volume so that the $p$-brane is treated as a $(p+1)$-instanton. The boundary states have the superspace interpretation of top or bottom states in a light-cone string superfield. The presence of a non-trivial open-string boundary condensate give rise to the familiar $D$-brane source terms that determine the (linearized)…
Light-cone quantization procedure recently presented is applied to the two-dimensional light-cone theories. By introducing the two distinct null planes it is shown that the modification term in the two-dimensional massless light-cone propagators suggested about twenty years ago vanishs.
A general procedure is introduced allowing for the infinite decomposition of nonlocal operators off the light--cone into operators of definite geometric twist.
The mechanism by which the physical vacuum can be different from the perturbative vacuum in the light-cone representation is described and illustrated.
In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.
Parity violation is a long standing problem in light-cone quantization. \REF\CPT{D. Soper, SLAC-REP-137, 1970, Chap. I . } \refend We propose a new quantization on the light-cone which treats both the $x^{+}$ and the $x^{-}$ coordinates as light-cone 'times.'This quantization respects both parity and time-reversal. We find that now both $P^{-}$ and $P^{+}$ become dynamical.
The gist of using the light cone gauge lies in the well known property of ghosts decoupling. But from the BRST point of view this is a stringency since for the construction of a nilpotent operator (from a Lie algebra) the presence of ghosts are mandatory. We will show that this is a foible which has its origins in the very fact of using just one light cone vector ($n_μ$) instead of working with both light cone vectors ($n_μ$ and $m_μ$) to fulfill the light cone base vectors. This will break out ghost decoupling from theory but allowing now a consistent BRST theory for the light cone gauge.
In this letter, we determine the particle and the string light cone in the pp-wave background. The result is a deformed version of the flat one. We point out the light cone exhibits an intriguing periodicity in the light cone time direction x^+ with a period \sim 1/ μ. Our results also suggest that a quantum theory in the pp-wave background can be formulated consistently only if the background is periodic in the light cone time x^+.
We give a relatively simple explanation of the light-cone supergraph prediction for the UV properties of the maximally supersymmetric theories. It is based on the existence of a dynamical supersymmetry which is not manifest in the light-cone supergraphs. It suggests that N=4 supersymmetric Yang-Mills theory is UV finite and N=8 supergravity is UV finite at least until 7 loops whereas the $n$-point amplitudes have no UV divergences at least until $L=n+3$. Here we show that this prediction can be deduced from the properties of light-cone supergraphs analogous to the light-by-light scattering eff…
Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1 superfields. In particular, superconformal polar multiplets are consistently defined for the first time. We present new 4D N = 2 superconformal sigma-models described by polar multiplets. Such sigma-models realize general superconformal couplings in projective superspace, but involve an infinite tale of auxiliary N = 1 superfields. The auxiliaries should be eliminated …
The vacuum problem of light-cone quantum field theory is reanalysed from a functional-integral point of view.
The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.
Recently suggested causal principal value and causal prescriptions for the "spurious singularity" in light-cone gauge theories are nothing but the different guises of usual Mandelstam-Leibbrandt prescription.
New prescription for the singularities of light-cone gauge theories is suggested. The new prescription provides Green's function which is identical with and different from that of Mandelstam-Leibbrandt prescription at $d=4$ and $d=2$ respectively.
Light cone form of field dynamics in anti-de Sitter spacetime is described. We also present light cone reformulation of the boundary conformal field theory representations. AdS/CFT correspondence between the bulk fields and the boundary operators is discussed.
It is well-known that additional constraints emerge in light cone coordinates. We enumerate the number of physical modes in light cone coordinates and compare it with conventional coordinates. We show that the number of Schrodinger modes is divided by two in light cone coordinates. We study the effect of this reduction in the number ladder operators acting on physical states of a system. We analyse the scaler, spinor and vector field theories carefully to see the effect of changes in the dynamical structure of these theories from the view point of the reduction of Schrodinger modes in light-co…
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