Light-cone Coordinates Research Articles

Massive fields in AdS from constructive holography

Collective field theory offers a constructive framework for exploring the AdS/CFT duality. In this article, we focus on constructing rotations within the light-front quantized collective field theory for the full set of spatial coordinates in the dual bulk AdS spacetime. Two intricate aspects require attention: how rotations involving the emergent holographic coordinate are implemented, and how rotations that involve the spatial coordinates participating in the construction of the light-cone coordinates X± are realized. Our construction is in agreement with Metsaev’s construction directly in the gravity theory. Additionally, we derive the eigenfunctions of the AdS mass operator, which dictate the GKPW rule for the emergent higher-dimensional theory.

Anatomy of null contractions

We introduce null contractions of the Poincare and relativistic conformal algebras. The longitudinal null contraction involves writing the algebra in lightcone coordinates and contracting one of the null directions. For the Poincare algebra, this yields two non-overlapping co-dimension one Carroll algebras. The transverse contraction is a limit on the spatial dimensions and yields two non-overlapping co-dimension one Galilean algebras. We find, similar to Susskind’s original observation of the non-relativistic case, that the Poincare algebra, written in the lightcone coordinates, naturally contains Carrollian sub-algebras in one lower dimension. The effect of the longitudinal contraction, which essentially focusses on the null direction, is to disentangle the two Carroll algebras that now correspond to the symmetries of the two null boundaries. The transverse contraction similarly separates the overlapping Galilean sub-algebras of the original Poincare algebra. We discuss aspects of the conformal case, where we get lower dimensional Carroll Conformal algebras and Schrödinger algebras.

Scalar propagator in a background gluon field beyond the eikonal approximation

We investigate the path integral representation of the scalar propagator in a background gluon field, extending beyond the eikonal approximation by considering all gauge field components and incorporating its x− dependence. Utilizing the worldline formalism, we integrate the Schwinger proper time to express the scalar propagator in light-cone coordinates, facilitating a direct comparison with known results in the literature. The derived propagator captures the change of longitudinal momentum of the projectile within the medium. In the high-energy limit, our result simplifies to the effective gluon propagator employed in the BDMPS-Z formalism. Hence, we propose that our outcome serves as a foundational point for investigating corrections to the BDMPS-Z spectrum arising from the longitudinal momentum transfer of the radiated gluon with the medium, as well as for studying collisional energy loss phenomena. Lastly, by employing an expansion around the classical saddle point solution, we systematically derive an eikonal expansion in inverse powers of the boost parameter, encompassing corrections related to longitudinal momentum transfer and interactions of the projectile with the transverse component of the field.

Quantum causality in κ-Minkowski and related constraints

We study quantum causal structures in κ-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the κ-Poincaré algebra. We show that the Lorentzian Spectral Triple must be twisted to accommodate the twisted nature of the derivations. We exhibit various interesting classes of causal functions, including an analog of the light-cone coordinates. We show in particular that the existence of a causal propagation between two pure states, the quantum analogs of points, can exist provided quantum constraints, linking the momentum and the space coordinates, are satisfied. One of these constraints is a quantum analog of the speed of light limit.

Numerical representation of tightly focused ultra-short laser pulses

A scheme for numerical representation for the fields of tightly focused laser pulses is presented going beyond the paraxial framework that gives accurate values up to near single-cycle pulses. The laser field is defined by a solution of the paraxial Helmholtz equation and a temporal pulse profile in light-cone coordinates, the fourth- and second-order corrections are provided for short pulses and vector beams, and the absolute error of these terms is presented. The method can give an accurate field description for any transverse electromagnetic mode, and it is suited for providing initial fields for existing solvers for Maxwell’s equations, such as in the particle-in-cell codes.

Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity

We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4D light-cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4D Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.

Scalar product according to Klein-Fock-Gordon equation in the context of light cone coordinates / Produto escalar associado a equação de Klein-Fock-Gordon no contexto de coordenadas de cone de luz

The objective of the present work is to didactically analyze, in the context of relativistic quantum mechanics, the algebraic structuring of the dot product between two quantum wavefunctions relative to a spin-0 quantum particle, assuming the light cone coordinates. For that, the linear momentum tensor is used in four dimensions, considering the description of the operational and quantum character of energy and linear momentum in three dimensions, as well as defining a pseudo volumetric probability density from which the product is reached scalar, properly written in terms of light cone coordinates.

Cosmological perturbations and invariant observables in geodesic lightcone coordinates

We consider a recent approach to the construction of gauge-invariant relational observables in gravity in the context of cosmological perturbation theory. These observables are constructed using a field-dependent coordinate system, which we take to be geodesic lightcone coordinates. We show that the observables are gauge-independent in the fully non-linear theory, and that they have the expected form when one adopts the geodesic lightcone gauge for the metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear order, and the Hubble rate — as measured both by geodesic observers and by observers co-moving with the inflaton — to second order. Moreover, we show that the well-known linearised equations of motion for the Sasaki-Mukhanov variable and the scalar constraint variables follow from the gauge-invariant Einstein's equations.

Leading and higher twist transverse momentum dependent parton distribution functions in the spectator model

Transverse momentum dependent parton distribution functions, also abbreviated as TMDs, offer a three-dimensional picture of hadrons by taking the intrinsic transverse momentum of the parton into consideration. Hence, they are very important for us to understand the structure of hadrons. In this article, we calculate and summarize all TMDs of quark through the spectator model, from twist-2 to twist-4. Especially, we give complete results of TMDs at twist-4. We adopt a general analytical framework to calculate TMDs, with both scalar and axial-vector spectators being considered. All TMDs are calculated analytically in the light-cone coordinate, and single gluon rescattering is considered to generate T-odd TMDs. T-even TMDs are also calculated to this level, maybe for the first time. Different from the traditional point of view, the twist-4 TMDs can contribute to some physical observables like azimuthal asymmetries. An approximate formula of the Sivers asymmetry, including twist-4 TMDs, is given.

Calculation of the creation and annihilation operators of a free particle in the light cone coordinate formalism

This work didactically presents the mathematical procedures required for the construction of the creation and annihilation operators for a free quantum particle considering the coordinates of the light cone. For that, the relationships between the aforementioned coordinates and the coordinates (ct, x, y, z) are listed, in addition to the use of the Klein-Gordon-Fock equation in the formalism of the light cone coordinates. Finally, the temporal evolution operator and the quantum operators of creation and annihilation of the integral type of motion are obtained.

Lepton pair production in ultraperipheral collisions

The lepton pair production in ultraperipheral collisions is studied in the classical field approximation. We derive a general form of the cross section in terms of photon distributions that depend on the transverse momentum and coordinate based on the wave packet form of nuclear wave functions. Such a general form of the cross section in the classical field approximation contains the results of the generalized equivalent photon approximation (EPA) as well as the corrections beyond EPA in the Born approximation. By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation. Our numerical results are consistent with current experimental data.

Cutting out the cosmological middle man: general relativity in the light-cone coordinates

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer’s light-cone and light propagation to obtain observables. Cosmological perturbation theory in the Friedmann–Lemaître–Robertson–Walker (FLRW) coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays toward the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to observables. This is possible if one works uniquely in such light-cone coordinates, thus completely bypassing the FLRW ‘middle-man’ coordinates. We first present in detail these light-cone coordinates, extending and generalizing the presently available material in the literature, and construct a particularly convenient subset for cosmological perturbation theory. We then express the Einstein and energy–momentum conservation equations in these coordinates at the fully non-linear level. This is achieved through a careful 2 + 1 + 1 decomposition which leads to relatively compact expressions and provides good control over the geometrical interpretation of the involved quantities. Finally, we consider cosmological perturbation theory to linear order, paying attention to the remaining gauge symmetries and consistently obtaining gauge-invariant equations. Moreover, we show that it is possible to implement statistical homogeneity on stochastic fluctuations, despite the fact that the coordinate system privileges the observer world-line.

Hamiltonian multiform description of an integrable hierarchy

Motivated by the notion of Lagrangian multiforms, which provide a Lagrangian formulation of integrability, and by the results of the authors on the role of covariant Hamiltonian formalism for integrable field theories, we propose the notion of Hamiltonian multiforms for integrable 1 + 1-dimensional field theories. They provide the Hamiltonian counterpart of Lagrangian multiforms and encapsulate in a single object an arbitrary number of flows within an integrable hierarchy. For a given hierarchy, taking a Lagrangian multiform as the starting point, we provide a systematic construction of a Hamiltonian multiform based on a generalization of techniques of covariant Hamiltonian field theory. This also produces two other important objects: a symplectic multiform and the related multi-time Poisson bracket. They reduce to a multisymplectic form and the related covariant Poisson bracket if we restrict our attention to a single flow in the hierarchy. Our framework offers an alternative approach to define and derive conservation laws for a hierarchy. We illustrate our results on three examples: the potential Korteweg–de Vries hierarchy, the sine-Gordon hierarchy (in light-cone coordinates), and the Ablowitz–Kaup–Newell–Segur hierarchy.

Scaling of PDFs, TMDs, and GPDs in soft-wall AdS/QCD

We explicitly demonstrate how to correctly define the hadronic parton distributions (PDFs, TMDs, and GPDs) in the soft-wall AdS/QCD approach, based on the use of a quadratic dilaton field, providing confinement and spontaneous breaking of conformal and chiral symmetries. The power behavior of parton distributions at large values of the light-cone variable is consistent with quark counting rules and Drell-Yan-West duality. All parton distributions are defined in terms of profile functions, which depend on the light-cone coordinate and are fixed from PDFs and electromagnetic form factors.

On the Galilean Duffin–Kemmer–Petiau equation in arbitrary dimensions

We obtain the representations of the Galilean covariant Duffin–Kemmer–Petiau equation in an arbitrary number of dimensions. Their purpose is to facilitate the study of nonrelativistic many-body systems with spinless and spin-one fields. A Galilean covariant formalism exploits the tensor structure of relativistic Lorentz-invariant theories by adding one extra spacelike coordinate and working with light-cone coordinates.

TT¯ deformations as TsT transformations

The relationship between $T\bar{T}$ deformations and the uniform light-cone gauge, first noted in arXiv:1804.01998, provides a powerful generating technique for deformed models. We recall this construction, distinguishing between changes of the gauge frame, which do not affect the theory, and genuine deformations. We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing. Exploiting a formal relation between uniform light-cone gauge and static gauge in a T-dual frame, we interpret such a change as a TsT transformation involving the two light-cone coordinates. In the static-gauge picture, the $T\bar{T}$ CDD factor then has a natural interpretation as a Drinfel'd-Reshetikhin twist of the worldsheet S matrix. To illustrate these ideas, we find the geometries yielding a $T\bar{T}$ deformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds.

Variational symmetries and conservation laws of the wave equation in one space dimension

The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether’s theorem yields the space of variational symmetries of the corresponding functional. The results are also presented for the standard space–time form of the wave equation.

Study of The Chiral Magnetic Effect in Light-cone coordinate from gauge/gravity duality

Study of The Chiral Magnetic Effect in Light-cone coordinate from gauge/gravity duality

Dynamical structure of fields in light cone coordinates

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-cone coordinates.

Non-equilibrium critical phenomena from probe brane holography in Schr\xf6dinger spacetime

We study the non-equilibrium steady-state phase transition from probe brane holography in z = 2 Schrödinger spacetime. Concerning differential conductivity, a phase transition could occur in the conductor state. Considering constant current operator as the external field and the conductivity as an order parameter, we derive scaling behavior of order parameter near the critical point. We explore the critical exponents of the nonequilibrium phase transition in two different Schrödinger spacetimes, which originated 1) from supergravity, and 2) from AdS blackhole in the light-cone coordinates. Interestingly, we will see that even at the zero charge density, in our first geometry, the dynamical critical exponent of z = 2 has a major effect on the critical exponents.