Light-cone Gauge Research Articles

A perturbative approach to the non-relativistic string spectrum

In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS5×S5 spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions.

Nicolai maps and uniqueness in the light-cone gauge

We compute the Nicolai map for the supersymmetric Yang-Mills theory, in the light-cone gauge, to the second order in the coupling constant for all critical dimensions (d = 3, 4, 6, 10). The process of integrating out unphysical degrees of freedom in this gauge, produces a four fermion interaction term. We show that, to the order investigated here, this term is harmless. We demonstrate the existence of a particularly ‘simple’ map in d = 4 in the light-cone gauge and address the issue of uniqueness in the context of the map. We also investigate the map in the light-cone superspace in d = 4.

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The Yang–Mills–Chern–Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi–Rouet–Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-functions and all anomalous dimensions to all orders in perturbation theory.

Inequivalent light-cone gauge-fixings of strings on AdSn×Sn backgrounds

Light-cone gauge-fixed sigma models on AdSn×Sn backgrounds play an important role in the integrability formulation of the AdS/CFT correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as TT¯, J˜Tτ, JTσ, and Jτ deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to AdS5×S5, compute the different light-cone gauge symmetry algebras, well known to be psu(2|2)⊕2⊕u(1)⊕2 for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models. Published by the American Physical Society 2024

Transversity generalized parton distributions in spin- 3/2 particles

The definitions of the quark and gluon transversity generalized parton distributions (GPDs) in spin-3/2 particles are obtained in the light-cone gauge. It is found that they contain 16 independent components for each parton. Their even or odd property is found in terms of a skewness variable, and the odd transversity GPDs vanish in the forward limit. There are 16 amplitudes with helicity flip of quark or gluon. We conclude that all the amplitudes, unpolarized, polarized, and transversity amplitudes, have a common factor F(ζ) carrying all the complex parts. Here, the variable ζ is the helicity difference ζ=(λ′−λ)−(μ′−μ) for the amplitude Aλ′μ′,λμ. This kinematical factor is associated with the transfer of the orbital angular momentum in the quark- and gluon-spin-3/2 particle scattering amplitudes. We also derive another main physical quantity, transversity distribution, from the transversity GPDs in the forward limit for the spin-3/2 particles. Published by the American Physical Society 2024

Elliptic deformations of the AdS3 × S3 × T4 string

Abstract With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

On mixed-flux worldsheet scattering in AdS3/CFT2

Strings on AdS3 × S3 × T4 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux are known to be classically integrable. This is a crucial property of this model, which cannot be studied by conventional worldsheet-CFT techniques. Integrability should carry over to the quantum level, and the worldsheet S matrix in the lightcone gauge is known up to the so-called dressing factors. In this work we study the kinematics of mixed-flux theories and consider a relativistic limit of the S matrix whereby we can complete the bootstrap program, including the dressing factors for fundamental particles and bound states. This provides an important test for the dressing factors of the full worldsheet model, and offers new insights on the features of the model when the amount of NSNS flux is low.

Light-cone gauge in non-relativistic AdS5×S5 string theory

We discuss the non-relativistic limit of string theory in AdS5×S5 for different choices of embedding coordinates. We show that, if we consider Cartesian coordinates, the action of fluctuations around the twisted BMN-like string found in arXiv:2109.13240 in uniform light-cone gauge becomes the one of free fields at large string tension and large AdS5 radius.

Superstrings on Penrose limits of AdS7 solutions

We consider the Penrose limit of AdS7 solutions of massive Type IIA supergravity. The resulting pp-wave geometry is supported by RR and NSNS fields. We quantize the Green-Schwarz superstring on the obtained pp-wave background, in the light-cone gauge.

Circuit complexity for coherent-thermal states in bosonic string theory

In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal string state and a thermal-coherent string state. We use the covariance matrix approach to calculate the circuit complexity of coherent-thermal string states. In this approach, we generate the optimal geodesics by a horizontal string generator, and then obtain the circuit complexity using the length of the minimal geodesics in the group manifold.

Superspace expansion of the 11D linearized superfields in the pure spinor formalism, and the covariant vertex operator

11D pure spinors have been shown to successfully describe 11D supergravity in a manifestly super-Poincaré covariant manner. The feasibility of its actual usage for scattering amplitude computations requires an efficient manipulation of the superfields defining linearized 11D supergravity. In this paper, we directly address this problem by finding the superspace expansions of these superfields, at all orders in θ, from recursive relations their equations of motion obey in Harnad-Shnider-like gauges. After introducing the 11D analogue of the 10D ABC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{ABC} $$\\end{document} superparticle, we construct, for the first time, a fully covariant vertex operator for 11D supergravity by making use of the linearized 11D superfields. Notably, we show that this vertex reproduces the Green-Gutperle-Kwon 11D operators in light-cone gauge.

Light-cone formalism for a point particle in a higher-spin background

We study propagation of a point particle in a massless higher-spin background employing the light-cone gauge approach. We find the point particle action and the associated phase space Poincare charges at the leading order in higher-spin fields. We also compare our results with the analogous covariant results available in the literature.

Toverline{T} flow as characteristic flows

We show that method of characteristics provides a powerful new point of view on Toverline{T} -and related deformations. Previously, the method of characteristics has been applied to Toverline{T} -deformation mainly to solve Burgers’ equation, which governs the deformation of the quantum spectrum. In the current work, we study classical deformed quantities using this method and show that Toverline{T} flow can be seen as a characteristic flow. Exploiting this point of view, we re-derive a number of important known results and obtain interesting new ones. We prove the equivalence between dynamical change of coordinates and the generalized light-cone gauge approaches to Toverline{T} -deformation. We find the deformed Lagrangians for a class of Toverline{T} -like deformations in higher dimensions and the ( Toverline{T} )α-deformation in 2d with generic α, generalizing recent results in [1] and [2].

Hadronic structure on the light front. II. QCD strings, Wilson lines, and potentials

This is the second paper on hadronic wave functions in the light-front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light-cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the light front.

Light-cone gauge massive and partially-massless fields in AdS(4)

Using light-cone gauge approach, bosonic and fermionic massive and partially-massless fields in AdS(4) space are considered. For such fields, light-cone gauge action is presented. Considering the massive and partially-massless fields in helicity basis and CFT adapted basis, two simple representations of spin operators entering the light-cone gauge action are discussed. The simple representations for the spin operators are obtained by using bosonic spinor-like oscillators. The bosonic spinor-like oscillators allow also us to treat the bosonic and fermionic fields on an equal footing.

General light-cone gauge approach to conformal fields and applications to scalar and vector fields

Totally symmetric arbitrary spin conformal fields propagating in the flat space of even dimension greater than or equal to four are studied. For such fields, we develop a general ordinary-derivative light-cone gauge formalism and obtain restrictions imposed by the conformal algebra symmetries on interaction vertices. We apply our formalism for the detailed study of conformal scalar and vector fields. For such fields, all parity-even cubic interaction vertices are obtained. The cubic vertices obtained are presented in terms of dressing operators and undressed vertices. We show that the undressed vertices of the conformal scalar and vector fields are equal, up to overall factor, to the cubic vertices of massless scalar and vector fields. Various conjectures about interrelations between the cubic vertices for conformal fields in conformal invariant theories and the cubic vertices for massless fields in Poincaré invariant theories are proposed.

The structure of interaction vertices in pure gravity in the light-cone gauge

The first truly non-MHV interaction vertices in the light-cone formulation of pure gravity appear at order 6. From a closed form expression, for gravitation in the light-cone gauge, we extract and present all 6-point interaction vertices. We invoke symmetry arguments to explain the structure of these vertices. Symmetry considerations also allow us to place constraints on the structure of all even- and odd-point vertices in the theory. The origin of MHV vertices within this formalism is also discussed.

Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production

Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable λ-deformed model for SU(2) together with a timelike coordinate. We construct the corresponding four-dimensional plane wave background (a deformation of the Nappi–Witten solution) keeping also post-plane wave corrections, as well as all the non-trivial λ-dependence. After imposing the classical light-cone gauge and the Virasoro constraints, we obtain an interacting field theory for the transverse physical modes which are massive. We explicitly demonstrate the absence of particle production to leading order in the large k-expansion. This is based crucially on the form of the interaction vertices and their dependence on the λ-deformation parameter. In addition, we compute the S-matrix for the two-particle elastic scattering exactly in λ and to leading order in the large k-expansion. Our method can be applied to any integrable theory with at least one isometry in order to check the classical integrability of the parent theory.

Celestial chiral algebras, colour-kinematics duality and integrability

We study celestial chiral algebras appearing in celestial holography, using the light-cone gauge formulation of self-dual Yang-Mills theory and self-dual gravity, and explore also a deformation of the latter. The recently discussed w1+∞ algebra in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality and the double copy relation between the self-dual theories. The W1+∞ deformation of w1+∞ arises from a Moyal deformation of self-dual gravity. This theory is interpreted as a constrained chiral higher-spin gravity, where the field is a tower of higher-spin components fully constrained by the graviton component. In all these theories, the chiral structure of the operator-product expansion exhibits the colour-kinematics duality: the implicit ‘left algebra’ is the self-dual kinematic algebra, while the ‘right algebra’ provides the structure constants of the operator-product expansion, ensuring its associativity at tree level. In a scattering amplitudes version of the Ward conjecture, the left algebra ensures the classical integrability of this type of theories. In particular, it enforces the vanishing of the tree-level amplitudes via the double copy.

Causality in string field theory

In this letter, we will investigate causality in string field theory using pp-wave light-cone gauge string field theory. We will generalise the Ramsey scheme to string field theory, and use it to analyze string field theoretical processes. An explicit characteristic function for interactive string field theory will be built using this string field theoretical Ramsey scheme. The average of the difference between the initial and final values of any operator described in string field theory will be obtained using this characteristic function. We will use the quantum information theoretical technique based on quantum Fisher information to extract information about such string field theoretical processes.