Light-cone Gauge Research Articles

The one-loop worldsheet S-matrix for the AdS n × S n × T 10−2n superstring

We compute the massive-sector worldsheet S-matrix for superstring theories in AdS(n) x S(n) x T(10-2n) (with n=2,3,5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3,5 cases it coincides with the one implied by the light-cone gauge symmetries with the dressing phases determined from the crossing equations. For the n=2,3 cases we observe that the massless modes decouple from the one-loop calculation of massive mode scattering, i.e. the 2n-dimensional supercoset sigma model and the full 10-dimensional superstring happen to have the same massive one-loop S-matrix.

Singularities, boundary conditions and gauge link in the light cone gauge

In this work, we first review the issues on the singularities and the boundary conditions in light cone gauge and how to regularize them properly. Then we will further review how these singularities and the boundary conditions can result in the gauge link at the infinity in the light cone direction in the Drell-Yan process. Except for reviewing, we also have verified that the gauge link at the light cone infinity has no dependence on the path not only for the Abelian field but also for non-Abelian gauge field.

On deformations of AdS n × S n supercosets

We study the deformed AdS 5 × S 5 supercoset model of arXiv:1309.5850 which depends on one parameter κ and has classical quantum group symmetry. We confirm the conjecture that in the “maximal” deformation limit, κ → ∞, this model is T-dual to “flipped” double Wick rotation of the target space AdS 5 × S 5, i.e. dS 5 × H 5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, κ → i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS 5 × S 5 superstring model. We also study in some detail similar deformations of the AdS 3 × S 3 and AdS 2 × S 2 supercosets. The bosonic part of the deformed AdS 3 × S 3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS 2 × S 2 case the role of the Fateev model is played by the 2d “sausage” model. The κ = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS n × S n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS 3 × S 3 with more than one parameter.

Light-cone gravity in AdS4

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.

On regularizing the infrared singularities in QCD NLO splitting functions with the new Principal Value prescription

We propose a modified use of the Principal Value prescription for regularizing the infrared singularities in the light-cone axial gauge by applying it to all singularities in the light-cone plus component of integration momentum. The modification is motivated by and applied to the re-calculation of the QCD NLO splitting functions for the purpose of Monte Carlo implementations. The final results agree with the standard PV prescription whereas contributions from separate graphs get simplified.

Quantum 3D tensionless string in light-cone gauge

We discuss the quantization of a tensionless closed string in light-cone gauge. It is known that by using a Hamiltonian BRST scheme the tensionless p-branes have no Lorentz anomaly in any space-time dimensions and no anomaly of space-time conformal symmetry in two dimensions. In this paper, we show that tensionless 3d strings in light-cone gauge also have no anomaly of space-time conformal symmetry. We also study the spectrum of a tensionless 3d closed string.

Comments on world-sheet form factors in AdS/CFT

We study form factors in the light-cone gauge world-sheet theory for strings in AdS5 ×S5. We perturbatively calculate the two-particle form factor in a closed sector to one-loop in the near-plane-wave limit and to two-loops in the Maldacena–Swanson limit. We also perturbatively solve the functional equation which follows from the form factor axioms for the world-sheet theory and show that the ‘minimal’ solution correctly reproduces the discontinuities of the perturbative calculations. Finally we propose a prescription, valid for polynomial orders of the inverse world-sheet length, for extracting the finite-volume world-sheet matrix element from the form factors and show that the two-excitation matrix element matches with the thermodynamic limit of the spin–chain description of certain tree-level SYM structure constants.

Calculation of QCD NLO Splitting Functions in the Light-cone Gauge: a New Regularization Prescription

We report on the progress in calculating NLO DGLAP splitting functions for $x<1$ using the New Principal Value prescription, which is a modification of the standard Principal Value approach proposed by Curci, Furmanski and Petronzio in 1980. The new prescription reproduces the standard results on the inclusive (integrated) level, but simplifies individual contributions and restricts the cancellations between real and virtual diagrams which makes it useful for Monte Carlo simulations.

An sl(2, $ \mathbb{R} $ ) current algebra from AdS 3 gravity

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary conditions consistent with the boundary terms introduced by Compère, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is a Virasoro algebra with Brown-Henneaux central charge c and an sl(2, $ \mathbb{R} $ ) current algebra with level given by c/6. The fully non-linear solution in Fefferman-Graham coordinates is also provided along with its charges.

Jacobi map and geodesic light-cone gauge: an exact solution

An exact expression for the Jacobi map is furnished. This result has been achieved thanks to the properties of the recently proposed geodesic light-cone gauge. From here, a non-perturbative expression for the area distance is given. It is remarkable that the expression we get nicely appears as the product of a pure source term times a pure observer one. This is true only in the particular gauge we adopt, as shown by transforming the area distance in the synchronous gauge and in the longitudinal one. The consistency among the two expressions is finally checked.

Microscopic unitary description of tidal excitations in high-energy string-brane collisions

Abstract The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high-energy behaviour of the covariant string amplitudes, showing how to take into account the energy factors that enhance the contribution of the longitudinally polarized massive states in a simple way.

An exact Jacobi map in the geodesic light-cone gauge

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map JAB(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge JAB factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system JAB is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked.Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.

Fluctuations of the initial color fields in high-energy heavy-ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^\tau=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.

Physics of the Gluon-Helicity Contribution to Proton Spin

The total gluon helicity in a polarized proton, measurable in high-energy scattering, is shown to be the large momentum limit of a gauge-invariant but nonlocal, frame-dependent gluon spin E × A⊥ in QCD. This opens a door for a nonperturbative calculation of this quantity in lattice QCD and also justifies using free-field expressions in the light-cone gauge as physical observables.

Multiloop amplitudes of light-cone gauge bosonic string field theory in noncritical dimensions

We study the multiloop amplitudes of the light-cone gauge closed bosonic string field theory for d ≠ 26. We show that the amplitudes can be recast into a BRST invariant form by adding a nonstandard worldsheet theory for the longitudinal variables X ± andthereparametrizationghostsystem. Theresultsobtainedinthispaperforbosonic strings provide a first step towards the examination whether the dimensional regularization works for the multiloop amplitudes of the light-cone gauge superstring field theory.

Probing parton orbital angular momentum in longitudinally polarized nucleon

While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured through twist-three GPDs. The second is the much-debated canonical OAM distribution natural in free-field theory and light-cone gauge. We show the latter in light-cone gauge can also be related to twist-three GPDs as well as quantum phase-space Wigner distributions, both being measurable in high-energy experiments.

Equivalence of 3D spinning string and superstring

We perform a light-cone gauge quantization of the Ramond-Ramond sector of the closed spinning string in three spacetime dimensions (3D). The spectrum is Lorentz invariant and identical to that of the 3D Green-Schwarz closed superstring with $ \mathcal{N} $ = 2 space-time supersymmetry, quantized in light-cone gauge.

Counterterms in gravity in the light-front formulation and a D = 2 conformal-like symmetry in gravity

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.

Worldsheet S-matrix of β-deformed SYM

We compute perturbative worldsheet S-matrix elements in the bosonic sector for β-deformed AdS/CFT in strong and weak ʼt Hooft coupling limits and compare with the exact S-matrix. For our purpose we take near BMN limit of TsT-transformed AdS5×S5 with the twisted boundary condition and compute the S-matrix on worldsheet using light-cone gauge fixed Lagrangian. For the weak coupling side, we compute the S-matrix in SU(3) sector by applying coordinate Bethe ansatz method to one-loop dilatation operator obtained from the deformed super Yang–Mills theory. These analysis support the conjectured exact S-matrix in the leading order for both sides of β-deformed AdS/CFT along with the appropriate twisted boundary conditions.

Worldsheet form factors in AdS/CFT

We formulate a set of consistency conditions appropriate to worldsheet form factors in the massive, integrable but nonrelativistic, light-cone gauge fixed ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ string theory. We then perturbatively verify that these conditions hold, at tree level in the near-plane-wave limit and to one loop in the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We further study the form factors in the weakly coupled dual description, verifying that the relevant conditions naturally hold for the one-loop Heisenberg spin chain. Finally, we note that the near-plane-wave expressions for the form factors, when further expanded in small momentum or, equivalently, large charge density, reproduce the thermodynamic limit of the spin-chain results at leading order.