21 pages, v2. the order-κ^2 form of the dynamical supersymmetry transformation corrected. v3. references and a few comments added, version to appear in JHEP
We use the Cremmer-Julia E_7(7) non-linear symmetry of N=8 Supergravity to derive its order $κ^2$ on-shell Hamiltonian in terms of one chiral light-cone superfield. By requiring that E_7(7) commute with the super-Poincare group, we deduce to lowest non-trivial order in $κ$, the light cone E_7(7) transformations of all fields of the theory, including the graviton. We then derive the dynamical supersymmetry transformation to order $κ^2$, and express the Hamiltonian as a quadratic form in the chiral superfield.
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.
The superfield light cone gauge formulation of $\mathcal{N} =4$ SYM in plane wave background is developed. We find a realization of superconformal symmetries in terms of a light cone superfield. An oscillator realization of superconformal symmetries is also obtained.
We constructe the $\mathcal{N}=1$ SYM lagrangian in light-cone gauge using chiral superfields instead of the standard vector superfield approach and derive the MHV lagrangian. The canonical transformations of the gauge field and gaugino fields are summarised by the transformation condition of chiral superfields. We show that $\mathcal{N}=1$ MHV super-vertices can be described by a formula similar to that of the $\mathcal{N}=4$ MHV super-amplitude. In the discussions we briefly remark on how to derive Nair's formula for $\mathcal{N}=4$ SYM theory directly from light-cone lagrangian.
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…
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…
The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2,2|N) symmetry should possess universal integrability properties for different N. We provide further support for this conjecture by computing a one-loop dilatation operator in all (super)symmetric Yang-Mills theories on the light-cone ranging from gluodynamics all the way to the maximally supersymmetric N=4 theory. We demonstrate that the dilatation operator takes a remarkably simple form when realized in the space spanned by single-trace products of superfields separated by light-l…
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 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…
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 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 calculate all the 2 to 2 scattering process in Yang-Mills theory in the Light Cone gauge, with the dimensional regulator as the UV regulator. The IR is regulated with a cutoff in $q^+$. It supplements our earlier work, where a Lorentz non-covariant regulator was used and the final results bear some problems in gauge fixing. Supersymmetry relations among various amplitudes are checked using the light cone superfields.
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 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.
Light cone gauge manifestly supersymmetric formulations of type IIB 10-dimensional supergravity in $AdS_5 \times S^5$ background and related boundary conformal field theory representations are developed. A precise correspondence between the bulk fields of IIB supergravity and the boundary operators is established. The formulations are given entirely in terms of light cone scalar superfields, allowing us to treat all component fields on an equal footing.
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.
Light-cone gauge manifestly supersymmetric formulation of type IIB 10-dimensional supergravity in $AdS_5 \times S^5$ background is discussed. The formulation is given entirely in terms of light-cone scalar superfield, allowing us to treat all component fields on an equal footing. Discrete energy spectrum of field propagating in AdS space is explained within the framework of light-cone approach. Light-cone gauge formulation of self-dual fields propagating in AdS space is developed. An conjectured interrelation of higher spin massless fields theory in AdS space-time and superstring theory in Min…
The symmetries of the N=4 SuperYang-Mills theory on the light-cone are discussed, solely in terms of its physical degrees of freedom. We derive explicit expressions for the generators of the PSU(2,2|4) superalgebra, both in the free theory, and to all orders in the gauge coupling of the classical theory. We use these symmetries to construct its Hamiltonian, and show that it can be written as a quadratic form of a fermionic superfield.
Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $α_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2πi}\ointλ^αd_α$. In this paper, a similarity transformation is found which simplifies the form of $Q$ and maps the light-cone description of the superstring vertices into DDF-like operators in the cohomology…
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 discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 supers…
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 show how to formulate $2$-dimensional supersymmetric $N=1,2$ theories, both massive and conformal, within a manifestly supersymmetric hamiltonian framework, via the introduction of a (super)-Poisson brackets structure defined on superfields. In this approach, as distinct from the previously known superfield hamiltonian formulations, the dynamics is not separated into two unrelated $2D$ light-cone superspaces, but is recovered by specifying boundary conditions at a given ``super-time" coordinate. So the approach proposed provides a natural generalization of canonical hamiltonian formalism. O…
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 use the plethystic exponential and the Molien-Weyl formula to compute the Hilbert series (generating funtions), which count gauge invariant operators in N=1 supersymmetric SU(N_c), Sp(N_c), SO(N_c) and G_2 gauge theories with 1 adjoint chiral superfield, fundamental chiral superfields, and zero classical superpotential. The structure of the chiral ring through the generators and relations between them is examined using the plethystic logarithm and the character expansion technique. The palindromic numerator in the Hilbert series implies that the classical moduli space of adjoint SQCD is an …
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…
$D$-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…
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 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.
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…
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…
We investigate the light-cone quantization of $ϕ^3$ theory in 1+1 dimensions with a regularization of discretized light-cone momentum $k^+$. Solving a second-class constraint associated with the $k^+=0$ mode, we show that the $k^+=0$ mode propagates along the internal lines of Feynman diagrams in any order of perturbation, hence our theory recovers the Lorentz invariance.
We derive a closed form expression for the light-cone Lagrangian describing pure gravity on a four-dimensional de Sitter background. We provide a perturbative expansion, of this Lagrangian, to cubic order in the fields.
It is shown that all bosonic and fermionic massive string models admit consistent light-cone formulations. This result is used to derive the spin generating functions of these models in four dimensions.
As part of program to quantize superstrings in AdS_5 x S^5 background in light cone approach we find the explicit form of the corresponding Green-Schwarz action in fermionic light-cone kappa-symmetry gauge. The resulting action is quadratic and quartic in fermions. In the flat space limit it reduces to the standard light-cone Green-Schwarz action, and also has the correct superparticle limit. We discuss fixing the bosonic light-cone gauge and a reformulation of the action in terms of 2-d Dirac spinors.
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…
The axial anomaly and fermion condensate in the light cone Schwinger model are studied following path integral methods. This formalism allows for a simple and direct calculation for these and other vacuum dependent phenomena.
We study the S-matrix of two-dimensional λϕ^4 theory in Discretized Light Cone Quantization and show how the correct continuum limit is reached for various processes in lowest order perturbation theory.
The six-dimensional (2,0) field theory admits a generalized ``noncommutative'' deformation associated with turning on a large null 3-form field strength. This theory is studied using its discrete light-cone formulation as quantum mechanics on a blow-up of the ADHM moduli space. We show how to interpret the ADHM manifold as configurations of open membranes, and check our results against basic space-time considerations.
It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.
The Casimir effect is investigated in light-cone quantization. It is shown that for spacelike separation of the walls enclosing the system the standard result for the pressure exerted on the walls is obtained. For walls separated in light-cone space direction no regularization of the quantum fluctuations exists which would yield a finite pressure. The origin of this failure and its implications for other vacuum properties are discussed by analyzing the Casimir effect as seen from a moving observer approaching the speed of light. The possibility for calculation of thermodynamic quantities in li…
In this work we present a possible way to relate the method of covariantizing the gauge dependent pole and the negative dimensional integration method for computing Feynman integrals pertinent to the light-cone gauge fields. Both techniques are applicable to the algebraic light-cone gauge and dispense with prescriptions to treat the characteristic poles.
The summation of all rainbow diagrams in QED in a strong magnetic field leads to a dynamical electron mass on the light-cone. Further contributions to this summation however can cause problems with light-cone singularities. It is shown that these problems are generally avoided by applying the point-splitting regularization to every diagram. The possibility of implementing this procedure into the Lagrangian of the theory is discussed.
It is developed the phase-space formulation for the Type IIA superstring on the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which the light-like directions are taken from the D=3 Minkowski boundary of AdS_4. After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.
We consider constructing a canonical quantum theory of the light-cone gauge ($A_-$=0) Schwinger model in the light-cone representation. Quantization conditions are obtained by requiring that translational generators $P_+$ and $P_-$ give rise to Heisenberg equations which, in a physical subspace, are consistant with the field equations. A consistent operator solution with residual gauge degrees of freedom is obtained by solving initial value problems on the light-cones. The construction allows a parton picture although we have a physical vacuum with nontrivial degeneracies in the theory.
We obtain a closed form expression for the Action describing pure gravity, in light-cone gauge, in a four-dimensional Anti de Sitter background. We perform a perturbative expansion of this closed form result to extract the cubic interaction vertex in this gauge.
