We analyze possible local extensions of the Poincaré symmetry in light-cone gravity in four dimensions. We use a formalism where we represent the algebra on the two physical degrees of freedom, one with helicity $2$ and the other with helicity $-2$. The representation is non-linearly realized and one of the light-cone momenta is the Hamiltonian, which is hence a non-linear generator of the algebra. We find that this can be locally realized and the Poincaré algebra extended to the BMS symmetry without any reference to asymptotic limits.
A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The $\mathcal{N}$-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the $\mathcal{N}=(1,2,4)$ super-BMS$_{3}$ appear as expansions of one Virasoro superalgebra. Interestingly, the $\mathcal{N}$-extended super-BMS$_{3}$ obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the $\mathcal{N}$-extended super Poincaré algebr…
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 …
A canonical realization of the BMS (Bondi-Metzner-Sachs) algebra is given on the phase space of the classical real Klein-Gordon field . By assuming the finiteness of the generators of the Poincaré group, it is shown that a countable set of conserved quantities exists (supertranslations); this set transforms under a particular Lorentz representation, which is uniquely determined by the requirement of having an invariant four-dimensional subspace, which corresponds to the Poincaré translations. This Lorentz representation is infinite-dimensional, non unitary, reducible and indecomposable. Its re…
We present the quantum $κ$-deformation of BMS symmetry, by generalizing the lightlike $κ$-Poincaré Hopf algebra. On the technical level, our analysis relies on the fact that the lightlike $κ$-deformation of Poincaré algebra is given by a twist and the lightlike deformation of any algebra containing Poincaré as a subalgebra can be done with the help of the same twisting element. We briefly comment on the physical relevance of the obtained $κ$-BMS Hopf algebra as a possible asymptotic symmetry of quantum gravity.
We construct two possible candidates for the non-relativistic $\mathfrak{bms}_4$ algebra in 4 space-time dimensions by contracting the original relativistic $\mathfrak{bms}_4$ algebra. The $\mathfrak{bms}_4$ algebra is infinite-dimensional, and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed $\mathfrak{nrbms}_4$ algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realisation of one these algebras in terms of the Fourier modes of a free Schrödinger field, mi…
Starting from the asymptotic kinematics of massless scalar fields near null infinity in any spacetime dimension, we build two higher-spin extensions of the Carrollian definition of the BMS group and its generalisations. The first extension exhibits conformal properties reminiscent of the singleton in Anti-de Sitter space. The second acts on the space of radiative solutions of the d'Alembert equation, i.e. on Sachs's representation of BMS, which we relate to the scalar massless Poincare representation and extend to any Carrollian manifold. The corresponding enveloping algebra is a higher-spin e…
We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincaré characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms_3 algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated character…
In this work we present a BMS-like ansatz for a Chern-Simons theory based on the semi-simple enlargement of the Poincaré symmetry, also known as AdS-Lorentz algebra. We start by showing that this ansatz is general enough to contain all the relevant stationary solutions of this theory and provides with suitable boundary conditions for the corresponding gauge connection. We find an explicit realization of the asymptotic symmetry at null infinity, which defines a semi-simple enlargement of the $\mathfrak{bms}_3$ algebra and turns out to be isomorphic to three copies of the Virasoro algebra. The f…
We consider two possible flat space limits of three dimensional $\mathcal{N} = (1,1)$ AdS supergravity. They differ by how the supercharges are scaled with the AdS radius $\ell$: the first limit (democratic) leads to the usual super-Poincare theory, while a novel `twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the $\mathcal{N}=(1,1)$ Virasoro …
The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein--Hilbert action reduces to a one-dimensional mechanical model. We have shown in [SciPost Phys. 10, 022 (2021), [2010.07059]] that this model exhibits a symmetry under the $(2+1)$-dimensional Poincaré group. Here we explain how this can be understood as a broken infinite-dimensional BMS$_3$ symmetry. This is done by reinterpreting the action for the model as a geometric action for BMS$_3$, where the configuration space variables are elements of the algebra $\mathfrak{bms}_3$ and…
New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincaré transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity c…
The Poincaré invariant vacuum is not unique in quantum gravity. The BMS supertranslation symmetry originally defined at null infinity is spontaneously broken and results in inequivalent Poincaré vacua. In this paper we construct the unique vacua which interpolate between past and future null infinity in BMS gauge and which are entirely characterized by an arbitary Goldstone boson defined on the sphere which breaks BMS invariance. We show that these vacua contain a defect which carries no Poincaré charges but which generically carries superrotation charges. We argue that there is a huge degener…
In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible Lie bialgebra structures and for selected examples, we explicitly construct the related Hopf algebras. Using cohomological arguments we show that this construction can always be performed by a so-called twist deformation. The resulting structures can be compared to the well-known $κ$-Poincaré Hopf algebras constructed on the finite dimensional Poincaré or (…
We elaborate on the proposal of flat holography in which four-dimensional physics is encoded in two-dimensional celestial conformal field theory (CCFT). The symmetry underlying CCFT is the extended BMS symmetry of (asymptotically) flat spacetime. We use soft and collinear theorems of Einstein-Yang-Mills theory to derive the OPEs of BMS field operators generating superrotations and supertranslations. The energy-momentum tensor, given by a shadow transform of a soft graviton operator, implements superrotations in the Virasoro subalgebra of $\mathfrak{bms_4}$. Supertranslations can be obtained fr…
The Poincare algebra of classical electrodynamics in one spatial dimension is studied using light-cone coordinates and ordinary Minkowski coordinates. We show that it is possible to quantize the theory by a canonical quantization procedure in a Poincare invariant manner on the light-cone. We also show that this is not possible when using ordinary coordinates. The physical reason of this anomaly is analysed.
BMS symmetry is a symmetry of asymptotically flat spacetimes in the vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been no…
We study string action with multiplet of $Θ$-terms added, which turns out to be closely related with the bosonic sector of D=11 superstring action [3,4]. Alternatively, the model can be considered as describing class of special solutions of the membrane. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.
We propose a new Doubly Special Relativity theory based on the generalization of the $κ$-deformation of the Poincaré algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincaré algebra and use it to derive the phase space commutation relations. As in the DSR based on the standard quantum $κ$-Poincaré algebra we find that the space time is non-commutative. We investigate the fate of the properties of Special Relativity in the null basis: the split of the algebra of Lorentz and momentum generators into kinematical and dynamical parts, the actio…
We calculate the coefficients of the leading non-global logarithms for the hemisphere mass distribution analytically at 3, 4, and 5 loops at large Nc . We confirm that the integrand derived with the strong-energy-ordering approximation and fixed-order iteration of the Banfi-Marchesini-Syme (BMS) equation agree. Our calculation exploits a hidden PSL(2,R) symmetry associated with the jet directions, apparent in the BMS equation after a stereographic projection to the Poincare disk. The required integrals have an iterated form, leading to functions of uniform transcendentality. This allows us to …
We derive light-cone cubic interaction vertices involving fermions and bosons of arbitrary spin by demanding closure of the Poincaré algebra. We derive the three-point scattering amplitude corresponding to these interaction vertices and find that they possess interesting factorization properties, identical to the case of three boson scattering.
We derive the quartic interaction vertex of pure Yang-Mills theory by demanding closure of the light-cone Poincaré algebra in four-dimensional Minkowski spacetime. This calculation explicitly shows why structure constants must satisfy the Jacobi identity. We then prove that corrections to the spin generator, for spin one at this order, vanish. We comment briefly on higher spin fields in this context.
I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras generalize the Fock space of massless particles. The algebra is realized in terms of operator valued measures on the momentum space dual to null infinity, and particles correspond to smearing these measures with delta functions. I conjecture that scattering amplitudes defined in terms of characteristic measures on finite spherical caps, the analog of Sterman-Weinber…
We reveal an $\mathfrak{iso}(2,1)$ Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincaré group ISO$(2,1)$, which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS${}_2$. At the Lagrangian level, this symmetry corresponds to Möbius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also nat…
Conformal Carrollian groups are known to be isomorphic to Bondi-Metzner-Sachs (BMS) groups that arise as the asymptotic symmetries at the null boundary of Minkowski spacetime. The Carrollian algebra is obtained from the Poincare algebra by taking the speed of light to zero, and the conformal version similarly follows. In this paper, we construct explicit examples of Conformal Carrollian field theories as limits of relativistic conformal theories, which include Carrollian versions of scalars, fermions, electromagnetism, Yang-Mills theory and general gauge theories coupled to matter fields. Due …
We construct Wigner's continuous spin representations of the Poincaré algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincaré algebra. If the light-cone translations are nilpotent, th…
We describe in detail two-parameter nonstandard quantum deformation of D=4 Lorentz algebra $\mathfrak{o}(3,1)$, linked with Jordanian deformation of $\mathfrak{sl} (2;\mathbb{C})$. Using twist quantization technique we obtain the explicit formulae for the deformed coproducts and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with dimensionless deformation parameter. Finally, we interpret $\mathfrak{o}(3,1)$ as the D=3 de-Sitter algebra and calculate the contraction limit …
In this short note we show, at the level of action principles, how the light-cone action of higher spin gauge fields can easily be obtained from the BRST formulation through the elimination of quartets. We analyze how the algebra of cohomology classes is affected by such a reduction. By applying the reduction to the Poincare generators, we give an alternative way of analyzing the physical spectrum of the Fronsdal type actions, with or without trace condition.
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…
We consider the AdS_5 x S^5 superstring in the light-cone gauge adapted to a massless geodesic in AdS5 in the Poincare patch. The resulting action has a relatively simple structure which makes it a natural starting point for various perturbative quantum computations. We illustrate the utility of this AdS light-cone gauge action by computing the 1-loop and 2-loop corrections to the null cusp anomalous dimension reproducing in a much simpler and efficient way earlier results obtained in conformal gauge. This leads to a further insight into the structure of the superstring partition function in n…
Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a {non-central} extension of the d=3 N=8 Poincare superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being {cubic} in the kinematical ones. The mass deformation picks a quaternionic direction, which breaks the SO(8) R-symmetry down to SO(4)xSO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations, to all orders in the mass para…
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.
Bosonic model inspired by D=11 superstring action is investigated. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.
The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this module is restricted by the requirement of the closure of the nonlinear realization of the Poincare algebra. The spin content of the model is analysed. In particular for D=4 the explicit formulae for the character generating functions of the open and closed massive strings are given and the spin spectrum of first 12 excited levels is calculated. It is shown th…
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…
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…
Infrared physics of QED and gravity from representation theory
SISSA（的里雅斯特国际高等研究院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Institut Denis Poisson, Université de Tours, Université d’Orléans, CNRS, IDP, UMR 7013（都灵大学、奥尔良大学、法国国家科学研究中心、德尼·普瓦松研究所）
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…
We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions $D$, with a particular emphasis on the case $D=5$. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS$_5$, which is realized non linearly, contains a four-fold family of angle-dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions $D…
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 undresse…
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…
Massive and massless arbitrary integer spin fields propagating in four-dimensional flat space are studied. The massive and massless fields are treated by using a light-cone gauge helicity basis formalism. Cubic cross-interactions between massive and massless fields and cubic interactions between massive fields are investigated. We introduce a classification of such cubic interactions and using our classification we build all cubic interaction vertices. Realization of generators of the Poincare algebra on space of interacting fields is found. As a by-product, some illustrative examples of light…
We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian…
We construct the E theory analogue of the particles that transform under the Poincare group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of E11 with its vector representation. We show that one such irreducible representation has only the degrees of freedom of eleven dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in E theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the li…
