General light-cone gauge approach to conformal fields and applications to scalar and vector fields
R. R. Metsaev
备注：
Comments: 39 pages, v2: Old results unchanged. New results and conclusions for cubic vertices for scalar and vector fields and many technical details in Secs.5,6,7 added. Conjecture about interrelations between cubic vertices for conformal fields and massless fields added. Appendices A,B,C and references added
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 Poincare invariant theories are proposed.
Light-cone formulation of conformal field theory in space-time of arbitrary dimension is developed. Conformal fundamental and shadow fields with arbitrary conformal dimension and arbitrary spin are studied. Representation of conformal algebra generators on space of conformal fundamental and shadow fields in terms of spin operators which enter in light-cone gauge formulation of field dynamics in AdS space is found. As an example of application of light-cone formalism we discuss AdS/CFT correspondence for massive arbitrary spin AdS fields and corresponding boundary CFT fields at the level of two…
Light-cone gauge formulation of fields in AdS space and conformal field theory in flat space adapted for the study of AdS/CFT correspondence is developed. Arbitrary spin mixed-symmetry fields in AdS space and arbitrary spin mixed-symmetry currents, shadows, and conformal fields in flat space are considered on an equal footing. For the massless and massive fields in AdS and the conformal fields in flat space, simple light-cone gauge actions leading to decoupled equations of motion are found. For the currents and shadows, simple expressions for all 2-point functions are also found. We demonstrat…
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…
In this work we present a proof of the discreteness of the spectrum for bosonic membrane, in a flat minkowski space. This may be useful to show the quantum mechanical consistence of others bosonics extended models. This proof includes the BRST residual symmetry and was directly performed over the discretized membrane model. The BRST residual invariant effective action is explicity constructed.
Light-cone gauge quantization procedures are given, for superstring theory on $AdS_3$ space charged with NS-NS background, both in NSR and GS formalism. The spacetime (super)conformal algebras are constructed in terms of the transversal physical degrees of freedom. The spacetime conformal anomaly agrees with that of covariant formalism, provided that the worldsheet conformal anomaly $c$ equals 26 or 15 for bosonic string or superstring, respectively. The spacetime (super)conformal field theory is found to correspond to orbifold construction on symmetric product space $\it{Sym_p} {\cal{M}}/Z_p$…
Aiming towards understanding the question of the discrete states in the light-cone gauge in the theory of two-dimensional strings with a linear background charge term, we study the path-integral formulation of the theory. In particular, by gauge fixing Polyakov's path-integral expression for the 2-d strings, we show that the light-cone gauge-fixed generating functional is the same as the conformal gauge-fixed one and is critical for the same value of the background charge (Q=2 $\sqrt 2 $). Since the equivalence is shown at the generating functional level, one expects that the spectra of the tw…
The classical tensionless string theory has the spacetime conformal symmetry. We expect and require that the quantum tensionless string theory has it too. In the BRST quantization method, the theory has no spacetime conformal anomaly in two dimensions. On the other hand, in the light-cone gauge quantization without the mode expansion, the theory in $D>3$ has the spacetime conformal anomaly in the traceless part of $[\mathcal{J}^{-I}, \mathcal{K}^{J}]$ in some operator order. In this paper, we consider a tensionless closed bosonic string in the light-cone gauge and investigate the spacetime con…
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.
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in the cosine of the scattering angle, with degree $\ell$ corresponding to the spin of the intermediate operator. The coefficients of these polynomials are obtained in a closed-form expression for arbitrary spacetime dimension $d > 2$. If the scaling dimension of the intermediate operator is large, the conformal block reduces to a Gegenbauer po…
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.
We present the Lagrangian and Feynman rules for QCD written in space-cone gauge and after eliminating unphysical degrees of freedom from the gluonic sector. The main goal is to clarify and allow for straightforward application of these Feynman rules. We comment on the connection between BCFW recursion relations and space-cone gauge.
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.
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.
Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the ``discretized'' light-cone quantization of gauge fields are discussed.
Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field…
The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.
We perform canonical analysis of new non-relativistic string action that was found recently in [arXiv:2107.00642 [hep-th]]. We also discuss its gauge fixed form.
We analyze the residual gauge freedom in light-cone electromagnetism in four dimensions. The standard boundary conditions involved in the so-called $lc_2$ formalism, which contains only the two physical degrees of freedom, allow for a subset of residual gauge transformations. We relax the boundary conditions imposed on the fields in order to obtain all the residual gauge transformations. We compute the canonical generators for Poincaré and gauge transformations with these relaxed boundary conditions. This enables us to distinguish between the trivial (proper) and large (improper) gauge transfo…
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.
We analyze the residual gauge freedom in gravity, in four dimensions, in the light-cone gauge, in a formulation where unphysical fields are integrated out. By checking the invariance of the light-cone Hamiltonian, we obtain a set of residual gauge transformations, which satisfy the BMS algebra realized on the two physical fields in the theory. Hence, the BMS algebra appears as a consequence of residual gauge invariance in the bulk and not just at the asymptotic boundary. We highlight the key features of the light-cone BMS algebra and discuss its connection with the quadratic form structure of …
We prove the Lorentz symmetry of supermembrane theory in the light cone gauge to complete the program initiated by de Wit, Marquard and Nicolai. We give some comments on extending the formulation to the M(atrix) theory.
In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we systematically study the symmetry structure of the theory in the SLC gauge both in the Lagrangian and the phase space formulations. After quantizing the theory in the latter formulation we construct the quantum Virasoro and the super-Poincare generators and clarify the closure properties of these symmetry algebras. Then by making full use of this knowledge we…
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.
Starting with the prepotential description of two-dimensional $(2,2)$ supergravity we use local supersymmetry transformations to go to light-cone gauge. We discuss properties of the theory in this gauge and derive Ward identities for correlation functions defined with respect to the induced supergravity action.
Vector supersymmetry is shown to exist also in light-cone gauge Chern-Simons theory. Using a gauge invariant regularization scheme, we demonstrate explicitly that the finite quantum correction to the coupling constant of Chern-Simons theory is intimately associated with the breaking of vector supersymmetry at the regularization level. The advantage of investigating such a quantum phenomenon in the light-cone gauge is emphasized and the BRST and vector supersymmetry invariance of quantum effective action is discussed.
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.
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.
Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.
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…
The one-loop quantum corrections of Chern-Simons spinor electrodynamics in the light-cone gauge has been investigated. We have calculated the vacuum polarization tensor, fermionic self-energy and on-shell vertex correction with a hybrid regularization consisting of a higher covariant derivative regularization and dimensional continuation. The Mandelstam-Leibbrandt prescription is used to handle the spurious light-cone singularity in the gauge field propagator. We then perform the finite renormalization to define the quantum theory. The generation of the parity-even Maxwell term and the arising…
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2 + 1 dimensional target space.
We present a representation independent solution to the continuum Schwinger model in light-cone ($A^+ = 0$) gauge. We then discuss the problem of finding that solution using various quantization schemes. In particular we shall consider equal-time quantization and quantization on either characteristic surface, $x^+ = 0$ or $x^- = 0$.
Quantization of the pure $1+1$ dimensional dilaton gravity is examined in the light-cone gauge. It is found that the total action including ghosts generates a $c=0$ free conformal field theory without modification of the classical action, which is required in the conformal gauge. We also study semiclassical equations of the dilaton gravity coupled to $N$ scalar fields. It is shown that the black hole singularity is not removed even for $N<24$ in the light-cone gauge. This indicates that the semiclassical analysis breaks down for small $N$.
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.
We review our recent work on M-theory compactifications on `toric' G_2 cones, a class of models which generalize those recently considered by Acharya and Witten and lead to chiral matter in four dimensions. We explain our criteria for identifying the gauge group content of such theories and briefly discuss the associated metrics.
We generalize to composite operators concepts and techniques which have been successful in proving renormalization of the effective Action in light-cone gauge. Gauge invariant operators can be grouped into classes, closed under renormalization, which is matrix-wise. In spite of the presence of non-local counterterms, an ``effective" dimensional hierarchy still guarantees that any class is endowed with a finite number of elements. The main result we find is that gauge invariant operators under renormalization mix only among themselves, thanks to the very simple structure of Lee-Ward identities …
Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.
We continue McCartor and Robertson's recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore to circumvent dealing with constrained systems, we construct the temporal gauge canonical formulation of the free electromagnetic field in auxiliary coordinates $x^μ=(x^-,x^+,x^1,x^2)$…
We reinvestigate the kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background in a version of the light-cone gauge. In the generalized light-cone gauge, the action has been written in the phase space variables. We convert it into the standard action written in terms of the fields and their derivatives. We obtain a Nambu-Goto type action which has the correct flat-space limit.
A new formulation of $c\leq 1$ matter coupled to 2D gravity is proposed. This model, being closely analogous to one in the Polyakov light-cone gauge, possesses well defined global properties which allow to calculate correlation functions. As an example, the three point correlation functions of discrete states are found.
We apply negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, being them originated from any gauge choice. In Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing for two-point functions without any kind of prescriptions, since NDIM can abandon such devices -- this calculation is the first test of our prescriptionless method beyond one-loop order; final…
We study the multiloop amplitudes of the light-cone gauge closed bosonic string field theory for $d \neq 26$. We show that the amplitudes can be recast into a BRST invariant form by adding a nonstandard worldsheet theory for the longitudinal variables $X^{\pm}$ and the reparametrization ghost system. The results obtained in this paper for bosonic 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.
Totally symmetric arbitrary spin fields in AdS space, conformal fields, conformal currents, and shadow fields in flat space are studied. Light-cone formulation for such fields, currents, and shadows is obtained. Use of the Poincare parametrization of AdS space allows us to treat fields in flat and AdS spaces on equal footing. Light-cone gauge realization of relativistic symmetries for fields, currents, and shadows is also obtained. The light-cone formulation for fields is obtained by using the gauge invariant Lagrangian which is presented in terms of the modified de Donder divergence, while th…
The Feynman amplitudes of light-cone gauge superstring field theory suffer from various divergences. In order to regularize them, we study the theory in linear dilaton background $Φ=-iQX^1$ with the number of spacetime dimensions fixed. We show that the theory with the Feynman $i\varepsilon\,(\varepsilon>0)$ and $Q^{2}>10$ yields finite results.
Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory for the longitudinal variables X^{\pm}, ψ^{\pm}. We show that with the transverse variables and the ghosts combined, it is possible to construct a nilpotent BRST charge.
This work describes the formulation of the manifestly ghost-free (spacetime) light-cone gauge for bosonic string theory with non-trivial spacetime metric, antisymmetric tensor, dilaton and tachyon fields. The action is a general two-dimensional sigma model, corresponding to a closed string theory with a second order action in the Polyakov picture. The spacetime fields must have a symmetry generated by a null, covariantly constant spacetime vector in order for the light-cone gauge to be accessible. Also, the theory must be Weyl invariant. The conditions for Weyl invariance are computed within t…
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.
The homogeneous inviscid Burgers equation which determines the spectrum of a TTbar deformed model has a natural interpretation as the condition of the gauge invariance of the target space-time energy and momentum of a (non-critical) string theory quantised in a generalised uniform light-cone gauge which depends on the deformation parameter. As a simple application of the light-cone gauge interpretation we derive the TTbar deformed Lagrangian for a system of any number of scalars, fermions and chiral bosons with an arbitrary potential. We find that the TTbar deformation is driven by the canonic…
Recently, models of two-dimensional dilaton gravity have been shown to admit classical black-hole solutions that exhibit Hawking radiation at the semi-classical level. These classical and semi-classical analyses have been performed in conformal gauge. We show in this paper that a similar analysis in the light--cone gauge leads to the same results. Moreover, quantization of matter fields in light--cone gauge can be naturally extended to include quantizing the metric field {\it à la} KPZ. We argue that this may provide a new framework to address many issues associated to black-hole physics.
The kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background is treated canonically in a version of the light-cone gauge. After reviewing the generalized light-cone gauge for a bosonic sigma model, we present the Hamiltonian dynamics of the Green-Schwarz action by using the transverse degrees of freedom. The remaining fermionic constraints are all second class, which we treat by the Dirac bracket. Upon quantization, all of the transverse coordinates are inevitably non-commutative.
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.
Light-cone form of field dynamics in anti-de Sitter space-time is developed. Using field theoretic and group theoretic approaches the light-cone representation for generators of anti-de Sitter algebra acting as differential operators on bulk fields is found. We also present light-cone reformulation of the boundary conformal field theory representations. Making use of these explicit representations of AdS algebra as isometry algebra in the bulk and the algebra of conformal transformations at the boundary a precise correspondence between the bulk fields and the boundary operators is established.
Feynman amplitudes of light-cone gauge string field theory for Type II superstrings are shown to be equivalent to those of the covariant first quantized formulation. In order to regularize the contact term divergences, we consider the theory in a linear dilaton background $Φ_{\mathrm{dilaton}}=-iQX^{1}$. We show that the scattering amplitudes are correctly reproduced in the limit $Q\to0$, even with Ramond sector external lines.
We study light-cone gauge string field theory in noncritical space-time dimensions. Such a theory corresponds to a string theory in a Lorentz noninvariant background. We identify the worldsheet theory for the longitudinal coordinate variables $X^\pm$ and study its properties. It is a CFT with the right value of Virasoro central charge, using which we propose a BRST invariant formulation of the worldsheet theory.
We propose a dimensional regularization scheme in the light-cone gauge NSR superstring field theory to regularize the divergences caused by the colliding supercurrents inserted at the interaction points. We study the tree amplitudes and show that our scheme actually regularize the divergences. We examine the four-point amplitudes for the NS-NS closed strings and find that the results in the first-quantized theory are reproduced without any counterterms.
