Dmitry Belyaev, Lars Brink, Sung-Soo Kim, Pierre Ramond
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.
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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…
We study the structure of the gauge sector of the Bagger-Lambert-Gustavsson (BLG) theory in the form proposed by van Raamsdonk, adapted to 3D, N=1 superspace. By using the novel Higgs mechanism proposed by Mukhi and Papageorgakis, we derive the manifestly N=1 supersymmetric higher-order terms (beyond the supersymmetric Yang-Mills action) that follow from the BLG theory in its expansion with respect to the inverse gauge coupling constant squared. We find that all those terms have at least one anti-commutator of the super-YM field strength superfields as a factor, and thus are reducible to the S…
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 …
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.
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.
We give a brief review of Bagger-Lambert-Gustavsson (BLG) model, with emphasis on its version invariant under the volume preserving diffeomorphisms (SDiff3) symmetry. We describe the on-shell superfield formulation of this SDiff3 BLG model in standard N=8, d=3 superspace, as well as its superfield action in the pure spinor N=8 superspace. We also briefly address the Aharony-Bergman-Jafferis-Maldacena (ABJM/ABJ) model invariant under $SU(M)_{k}\times SU(N')_{-k}$ gauge symmetry, and discuss the possible form of their N=6 and, for the case of Chern-Simons level k=1,2, N=8 superfield equations.
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 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.
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。
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…
In this paper we analyse the Bagger-Lambert-Gustavsson (BLG) theory in $\mathcal{N} =1$ superspace. Furthermore, we will construct the BRST transformations for this theory. These BRST transformations will be integrated out to obtain the finite field dependent version of BRST (FFBRST) transformations. We will also analyse the effect of the FFBRST transformations on the effective action. We will thus show that the FFBRST transformations can be used to relate generating functionals of the BLG theory in two different gauges.
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.
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.
We present the light-cone gauge fixed Lagrangian for the M5-brane; it has a residual `exotic' gauge invariance with the group of 5-volume preserving diffeomorphisms, SDiff(5), as gauge group. For an M5-brane of topology R2 x M3, for closed 3-manifold M3, we find an infinite tension limit that yields an SO(8)-invariant (1+2)-dimensional field theory with `exotic' SDiff(3) gauge invariance. We show that this field theory is the Carrollian limit of the Nambu bracket realization of the `BLG' model for multiple M2-branes.
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…
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.
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。
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.}
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…
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 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…
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…
We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal sigma-model is superconformal. Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahl…
$D$-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)…
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 …
Using Lorentz covariant spinor helicity formalism we reorganize the unitary scalar superfield light-cone path integral for the N=4 supersymmetric Yang-Mills theory. In new variables in the chiral Fourier superspace the quadratic and cubic parts of the classical action have manifest Lorentz, kinematical and dynamical supersymmetry, with the exception of terms which contribute only to the contact terms in the supergraphs with propagators shrinking to a point. These terms have the same structure as supergraphs with quartic light-cone vertices, which break dynamical supersymmetry. We present evide…
By compactifying the Bagger-Lambert-Gustavsson model on $\mathbb{R}^{1,1} \times S^1$, we obtain a new two dimensional massless field theory with dynamical fields valued in the Lie 3-algebra $\mathcal{A}$ coupled with an SO(1,1) scalar and vector field which are valued in the set $End(\mathcal{A})$ of the endomorphisms of the Lie 3-algebra. In the limit $g_{BLG} \to \infty$ the theory reduces to a supersymmetric Lie 3-valued generalization of the Green-Schwarz superstring in the light-cone gauge.
We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS_4 x CP^3. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the kappa-symmetry gauge condition t…
We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level ampli…
We employ the light-cone formalism to construct in the (super) Yang-Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N=4 Yang-Mills theory it exhausts all Wilson operators of the maximal Lorentz spin while in nonsupersymmetric Yang-Mills theory it is restricted to the sector of maximal helicity gluonic operators. We show that the dilatation operator in all N-extended super Yang-Mills theories is given by the same integral operator which acts on the (N+1)-dimensional superspac…
We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS5 x S5. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function 4F3. We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Luescher approaches to the finite-size spectral problem. They…
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