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Geometric tool kit for higher spin gravity (part III): An introduction to the general theory of connections on fibre bundles
Xavier Bekaert
These notes provides an introduction to a wide variety of notions of connection that appear in the contemporary mathematical literature. Besides the familiar Ehresmann connections…
Spinor-helicity formalism for continuous-spin particles
Thomas Basile, Xavier Bekaert, Felipe Figueroa +1
We propose a new formulation of continuous-spin particles (CSP) with the help of a single two-component spinor to build asymptotic states. This formulation allows to write down amp…
A geometrical invitation to BMS group theory
Xavier Bekaert, Yannick Herfray, Lea Mele +1
In these lecture notes, a group-theoretical introduction to BMS symmetries is provided in a self-contained manner. More precisely, all definitions and structures are purely based o…
Higher-Spin Poisson Sigma Models and Holographic Duality for SYK Models
Xavier Bekaert, Alexey Sharapov, Evgeny Skvortsov
SYK models provide an interesting playground for exploring the correspondence. We focus on a class of SYK models that exhibit higher-spin symmetry, whose gravity sect…
BMS representations for generic supermomentum
Xavier Bekaert, Yannick Herfray
We revisit the classification, and give explicit realisations, of unitary irreducible representations of the BMS group. As compared to McCarthy's seminal work, we make use of a uni…
Classification of Conformal Carroll Algebras
Hamid Afshar, Xavier Bekaert, Mojtaba Najafizadeh
We classify a one-parameter family, , of conformal extensions of the Carroll algebra in arbitrary dimension with being the anisotropic scaling expon…
Asymptotic behaviour of massless fields and kinematic duality between interior null cones and null infinity
Xavier Bekaert, S. I. Aadharsh Raj
The relation between two branches of solutions (radiative and subradiative) of wave equations on Minkowski spacetime is investigated, for any integer spin, in flat Bondi coordinate…
Holographic Carrollian Conformal Scalars
Xavier Bekaert, Andrea Campoleoni, Simon Pekar
We provide holographic realisations in Minkowski spacetime of a free conformal Carrollian scalar field living at null infinity. To this end, we first show that the electric and mag…
Geometric tool kit for higher spin gravity (part II): An introduction to Lie algebroids and their enveloping algebras
Xavier Bekaert
These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras and their universal envelopes. This review is motivated by the speculation that higher-sp…
Ambient-space variational calculus for gauge fields on constant-curvature spacetimes
Xavier Bekaert, Nicolas Boulanger, Maxim Grigoriev +1
We propose a systematic generating procedure to construct free Lagrangians for massive, massless and partially massless, totally-symmetric tensor fields on starting fro…
Geometric tool kit for higher spin gravity (part I): An introduction to the geometry of differential operators
Xavier Bekaert
These notes provide an introduction to the algebra and geometry of differential operators and jet bundles. Their point of view is guided by the leitmotiv that higher-spin gravity t…
Carrollian conformal scalar as flat-space singleton
Xavier Bekaert, Andrea Campoleoni, Simon Pekar
We show that, in any space-time dimension, the on-shell (electric) conformal Carrollian scalar can be interpreted as the flat-space limit of the singleton representation of the con…
Massless Scalars and Higher-Spin BMS in Any Dimension
Xavier Bekaert, Blagoje Oblak
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…
Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry
Xavier Bekaert, Nicolas Boulanger, Andrea Campoleoni +5
Higher Spin Gravity refers to extensions of gravity including at least one field of spin greater than two. These extensions are expected to provide manageable models of quantum gra…
Notes on higher-spin diffeomorphisms
Xavier Bekaert
Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem wh…
On BF-type higher-spin actions in two dimensions
K. B. Alkalaev, Xavier Bekaert
We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together w…
Towards higher-spin AdS/CFT holography
Konstantin Alkalaev, Xavier Bekaert
We aim at formulating a higher-spin gravity theory around AdS relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins…
Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
Thomas Basile, Xavier Bekaert, Euihun Joung
The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their charact…
Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras
Thomas Basile, Xavier Bekaert, Euihun Joung
We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dua…
Continuous-spin field propagator and interaction with matter
Xavier Bekaert, Jihad Mourad, Mojtaba Najafizadeh
Action principles for the single and double valued continuous-spin representations of the Poincare group have been recently proposed in a Segal-like formulation. We address three r…
Higher Spin Extension of Fefferman-Graham Construction
Xavier Bekaert, Maxim Grigoriev, Evgeny D. Skvortsov
Fefferman-Graham ambient construction can be formulated as -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits…
Elementary particles with continuous spin
Xavier Bekaert, Evgeny D. Skvortsov
Classical results and recent developments on the theoretical description of elementary particles with "continuous" spin are reviewed. At free level, these fields are described by u…
Mixed-symmetry fields in de Sitter space: a group theoretical glance
Thomas Basile, Xavier Bekaert, Nicolas Boulanger
We rederive the characters of all unitary irreducible representations of the -dimensional de Sitter spacetime isometry algebra , and propose a dictiona…
Higher Spin Double Field Theory : A Proposal
Xavier Bekaert, Jeong-Hyuck Park
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each…