Carroll fermions of arbitrary spin
Electric and magnetic Carrollian actions for fermions of arbitrary spin in any spacetime dimension are defined as inequivalent $c \to 0$ limits of the relativistic Fang-Fronsdal actions.
hep-th↗
arXiv subjects
Andrea Campoleoni
Publications and source records attributed to Andrea Campoleoni.
Flat from AdS: in any dimension and for any spin
The space of solutions to the free equations of motion for massless fields of arbitrary integer spin in Minkowski spacetime is recovered as a smooth limit of the anti-de Sitter solution space for any even spacetime dimension. The infinite set of boundary data near null infinity that characterise solutions in Minkowski spacetime is obtained from an expansion of the anti-de Sitter source and vev in powers of the cosmological constant. In particular, the source gives rise to the analogue of the gravitational shear tensor, while the vev yields the analogues of the mass and angular-momentum aspects, as well as the subleading infinite tower of boundary data. These identifications are further supported by the branching of the source and vev into representations of the Lorentz algebra identified with the conformal algebra of the celestial sphere.
hep-th↗
Asymptotically-FLRW$_3$ spacetimes
We introduce three-dimensional asymptotically-FLRW spacetimes as a simplified setting in which to study asymptotic symmetries and radiation in cosmology. Their asymptotic symmetry group is $\text{BMS}_3^k$, a one-parameter deformation of $\text{BMS}_3$ controlled by the matter equation of state with parameter $k$, in line with the four-dimensional construction of Bonga and Prabhu. We analyze in detail the case of a scalar field matter source, which allows us to fully characterize the solution space and the boundary charges. In particular, we point out that the proper identification of the Bondi mass and angular momentum aspects in the metric requires a careful analysis which had not been laid out so far, even in the existing four-dimensional literature. When superrotations are present, the model exhibits subtleties similar to those appearing when dealing with ''generalized BMS'' asymptotic symmetries in the four-dimensional case, and this requires a covariant definition of the news. We identify covariant notions of news, as well as of mass and angular momentum aspects by studying the vacuum structure, namely the orbits of the vacuum solution under finite $\text{BMS}_3^k$ transformations, and study the Wald-Zoupas prescription for the charges. We also show that these covariant aspects naturally appear in the Cotton scalars, which are the three-dimensional analogues of the Weyl scalars. Finally, we use these quantities to provide a first example of exactly conserved non-linear Newman-Penrose charges in three-dimensional gravity.
gr-qc↗
Finite actions and asymptotic charges at null infinity for any spin
We identify boundary terms renormalizing the free on-shell actions for massless fields of arbitrary spin, including electromagnetism and linearized gravity, with boundary conditions allowing for supertranslation-like asymptotic symmetries. Our focus is on null infinity, in any spacetime dimensions. We also comment on the renormalization of the corresponding asymptotic charges.
hep-th↗
Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit.
cond-mat.str-el↗
Higher-spin gauge theories in three spacetime dimensions
These lecture notes provide an introduction to higher-spin gauge theories in three spacetime dimensions, with a focus on their asymptotic symmetries, their holographic description in terms of conformal field theories with W-symmetries as well as on their couplings to scalar matter.
hep-th↗
Carroll Fermions
Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a reducible but indecomposable representation of the Carroll group. We also build action principles for all Carroll fermions we introduce; in particular, in even dimensions we provide an action principle for a minimal magnetic Carroll fermion, having the same number of components as a Dirac spinor. We then explore the coupling of these fermions to magnetic Carroll gravity in both its first-order and second-order formulations.
hep-th↗
Holographic Carrollian Conformal Scalars
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 magnetic limits of a relativistic conformal scalar are equivalent and we study the representation of the Carroll, Poincaré and BMS algebras that is realised on the resulting solution space. We then realise it as a quotient of the solution space of a free massless scalar in Minkowski spacetime with unusual falloff, in full analogy with the interpretation of Dirac's singleton as a shortened scalar in Anti de Sitter spacetime.
hep-th↗
Renormalization of spin-one asymptotic charges in AdS$_D$
We study the renormalized action and the renormalized presymplectic potential for Maxwell fields on Anti de Sitter backgrounds of any dimensions. We then use these results to explicitly derive finite boundary charges for angle-dependent asymptotic symmetries. We consider both Poincaré and Bondi coordinates, the former allowing us to control the systematics for arbitrary $D$, the latter being better suited for a smooth flat limit.
hep-th↗
Flat from anti-de Sitter
Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of the asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy--momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman--Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.
hep-th↗
Strange higher-spin topological systems in 3D
Motivated by the generation of action principles from off-shell dualisation, we present a general class of free, topological theories in three dimensional Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two case, we recover a dual reformulation of the triplet system already known, while the higher-spin systems that we obtain seem to be new. They are associated with wild quivers. We study in which situations these exotic (or strange) higher-spin models can be extended to dS${}_3$ and AdS${}_3$ backgrounds, revealing that the flat limit of such models, when they exist, admits a one-parameter freedom. Interactions are studied in the simplest higher-spin case featuring spin-2 and spin-3 fields. We then give several higher-spin generalisations of these strange systems.
hep-th↗
New higher-spin curvatures in flat space
It was shown that the Lie algebra underlying higher-spin holography admits a contraction including a Poincaré subalgebra in any space-time dimensions. The associated curvatures, however, do not reproduce upon linearisation those that are usually employed to formulate the equations of motion of free massless particles in Minkowski space. We show that, despite this mismatch, the new linearised curvatures can also be used to describe massless higher-spin fields. This suggests a new way to build interacting higher-spin gauge theories in Minkowski space that may admit a holographic description.
hep-th↗
A note on the admissibility of complex BTZ metrics
We perform a nontrivial check of Witten's recently proposed admissibility criterion for complex metrics. We consider the `quasi-Euclidean' metrics obtained from continuing the BTZ class of metrics to imaginary time. Of special interest are the overspinning metrics, which are smooth in this three-dimensional context. Their inclusion as saddle points in the gravitational path integral would lead to puzzling results in conflict with those obtained using other methods. It is therefore encouraging that the admissibility criterion discards them. For completeness, we perform an analysis of smoothness and admissibility for the family of quasi-Euclidean BTZ metrics at all values of the mass and angular momentum.
hep-th↗
Carrollian conformal scalar as flat-space singleton
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 conformal algebra. In fact, a recently proposed higher-spin algebra for Minkowski spacetime amounts to the Poincaré enveloping algebra on the corresponding module. This higher-spin algebra is a contraction of that entering Vasiliev's equations, which can be constructed analogously from the singleton representation of the conformal algebra. We also show that the higher-spin extension of the Poincaré algebra we consider is a subalgebra of all symmetries of the conformal Carrollian scalar, given by a higher-spin version of the (extended) BMS algebra.
hep-th↗
Infinite distances in multicritical CFTs and higher-spin holography
We investigate the swampland distance conjecture in higher-spin gravity. To this end, we study multicritical generalizations of large-$N$ vector models, bosonic and fermionic, and we compute the quantum information distance along selected renormalization-group trajectories toward the higher-spin limit. In striking contrast to the expected exponential decay of higher-spin masses or anomalous dimensions, we find that infinite-distance limits in these models lead to a power-like decay. This suggests that stringy exponential decays are characteristic of matrix-like gauge theories, rather than vector models. We corroborate this notion studying the information distance along coupling variations in Chern-Simons-matter CFTs, where matrix-like degrees of freedom dominate over vector-like ones.
hep-th↗
Holographic Lorentz and Carroll Frames
Relaxing the Bondi gauge, the solution space of three-dimensional gravity in the metric formulation has been shown to contain an additional free function that promotes the boundary metric to a Lorentz or Carroll frame, in asymptotically AdS or flat spacetimes. We pursue this analysis and show that the solution space also admits a finite symplectic structure, obtained taking advantage of the built-in ambiguities. The smoothness of the flat limit of the AdS symplectic structure selects a prescription in which the holographic anomaly appears in the boundary Lorentz symmetry, that rotates the frame. This anomaly turns out to be cohomologically equivalent to the standard holographic Weyl anomaly and survives in the flat limit, thus predicting the existence of quantum anomalies in conformal Carrollian field theories. We also revisit these results in the Chern--Simons formulation, where the prescription for the symplectic structure admitting a smooth flat limit follows from the variational principle, and we compute the charge algebra in the boundary conformal gauge.
hep-th↗
Magnetic Carrollian gravity from the Carroll algebra
We explicitly establish the equivalence between the magnetic Carrollian limit of Einstein gravity defined through the Hamiltonian formalism and the Carrollian theory of gravity defined through a gauging of the Carroll algebra along the lines of standard Poincaré (or (A)dS) gaugings.
hep-th↗
Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry
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 gravity thanks to the infinite-dimensional (higher spin) gauge symmetry constraining them. One of the key aspects of Higher Spin Gravity/Symmetry is the range and diversity of topics it embraces: (a) higher spin fields play a role in quantum gravity, AdS/CFT, string theory and are expected to have important consequences in cosmology and black hole physics; (b) higher spin symmetry finds applications in Conformal Field Theories, condensed matter systems and dualities therein; (c) these models often rely on tools developed in the study of the mathematical foundations of QFT or in pure mathematics: from deformation quantization and non-commutative geometry to conformal geometry, graded geometry (including BV-BRST quantization), and geometry of PDEs. Recent exciting applications also involve (d) modelling the coalescence of black hole binaries as scattering of massive higher spin particles.
hep-th↗