We study the dynamics of planons, particles whose mobility is restricted to a plane, through the classification of coadjoint orbits and unitary irreducible representations of the centrally extended planon group. Planons are closely related to Galilei/Bargmann symmetries and, remarkably, the often-ignored massless coadjoint orbits of the Galilei group play a central rôle in their description. We thereby provide a nontrivial physical interpretation of these orbits. We further construct classical and quantum dipoles as bound states of monopoles, where the restricted planar motion arises from a novel mixed Carroll-Galilei symmetry. We also argue that the simplest and already experimentally realised systems with Carroll symmetry are in crystals.

United Kingdom

José Figueroa-O’Farrill

Italy

Simon Pekar

Chile

Austria

Alfredo Pérez

Stefan Prohazka

Planons and their Carroll-Galilei symmetries

We consider quantum gravity with zero cosmological constant in three dimensions. First, we show that pure quantum gravity can be written as a magnetic Carrollian theory living on null infinity, described by Schwarzian-like degrees of freedom. Next, we couple quantum gravity to massless matter. Transition amplitudes exhibit several features that resemble soft graviton physics in four dimensions, despite the absence of a propagating graviton. As in four dimensions, we find three equivalent results: a soft graviton theorem, an infinite-dimensional BMS asymptotic symmetry, and a gravitational memory effect. We also resolve some extant puzzles concerning the partition function and Hilbert space of pure 3d gravity with zero cosmological constant.

United States

Jordan Cotler

Canada

Kristan Jensen

Max Riegler

Belgium

Jakob Salzer

Soft gravitons in three dimensions

Carrollian field theories have recently emerged as a candidate dual to flat space quantum gravity. We carefully quantize simple two-derivative Carrollian theories, revealing a strong sensitivity to the ultraviolet. They can be regulated upon being placed on a spatial lattice and working at finite inverse temperature. Unlike in conventional field theories, the details of the lattice-regulated Carrollian theories remain important at long distances even in the limit that the lattice spacing is sent to zero. We use that limit to define interacting continuum models with a tractable perturbative expansion. The ensuing theories are those of generalized free fields, with non-Gaussian correlations suppressed by positive powers of the lattice spacing, and an unbroken supertranslation symmetry.

Amir Raz

Quantizing Carrollian field theories

In theories with conserved dipole moment, isolated charged particles (fractons) are immobile, but dipoles can move. We couple these dipoles to the fracton gauge theory and analyze the universal infrared structure. This uncovers an observable double kick memory effect which we relate to a novel dipole soft theorem. Together with their asymptotic symmetries this constitutes the first realization of an infrared triangle beyond Lorentz symmetry. This demonstrates the robustness of these IR structures and paves the way for their investigation in condensed matter systems and beyond.

France

Ali Seraj

Fracton Infrared Triangle

Motivated by flat space holography, we demonstrate that massive spin-s fields in Minkowski space near timelike infinity are massive carrollian fields on the carrollian counterpart of anti-de Sitter space called Ti. Its isometries form the Poincaré group, and we construct the carrollian spin-s fields using the method of induced representations. We provide a dictionary between massive carrollian fields on Ti and massive fields in Minkowski space, as well as to fields in the conformal primary basis used in celestial holography. We show that the symmetries of the carrollian structure naturally account for the BMS charges underlying the soft graviton theorem. Finally, we initiate a discussion of the correspondence between massive scattering amplitudes and carrollian correlation functions on Ti, and introduce physical definitions of detector operators using a suitable notion of conserved carrollian energy-momentum tensor.

Denmark

Emil Have

Kevin Nguyen

Massive carrollian fields at timelike infinity

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Brazil

V. Prata

A. Santos

Faqir Khanna

Stefan–Boltzmann law and Casimir effect for dark photons

We classify and relate unitary irreducible representations (UIRs) of the Carroll and dipole groups, i.e., we define elementary quantum Carroll and fracton particles and establish a correspondence between them. Whenever possible, we express the UIRs in terms of fields on Carroll/Aristotle spacetime subject to their free field equations.

Quantum Carroll/fracton particles

We exploit the close relationship between the Carroll and fracton/dipole algebras, together with the method of coadjoint orbits, to define and classify classical Carroll and fracton particles. This approach establishes a Carroll/fracton correspondence and provides an answer to the question “What is a fracton?”.

Carroll/fracton particles and their correspondence

We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding to a homogeneous space. What the gauging procedure amounts to is the construction of a Cartan geometry modelled on that Klein geometry, with the gauge field defining a Cartan connection. The lagrangian itself consists of all gauge-invariant top-forms constructed from the Cartan connection and its curvature. After demonstrating that this procedure produces four-dimensional General Relativity upon gauging Minkowski spacetime, we proceed to gauge all four-dimensional maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter-Carroll and the lightcone. For the first three of these spaces, our lagrangians generalise earlier first-order lagrangians. The resulting theories of carrollian gravity all take the same form, which seems to be a manifestation of model mutation at the level of the lagrangians. The odd one out, the lightcone, is not reductive and this means that although the equations of motion take the same form as in the other cases, the geometric interpretation is different. For all carrollian theories of gravity we obtain analogues of the Gauss-Bonnet, Pontryagin and Nieh-Yan topological terms, as well as two additional terms that are intrinsically carrollian and seem to have no lorentzian counterpart. Since we gauge the theories from scratch this work also provides a no-go result for the electric carrollian theory in a first-order formulation.

The gauging procedure and carrollian gravity

We show that the geometry of the asymptotic infinities of Minkowski spacetime (in d + 1 dimensions) is captured by homogeneous spaces of the Poincaré group: the blow-ups of spatial (Spi) and timelike (Ti) infinities in the sense of Ashtekar-Hansen and a novel space Ni fibering over   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$ . We embed these spaces à la Penrose-Rindler into a pseudo-euclidean space of signature (d + 1, 2) as orbits of the same Poincaré subgroup of O(d + 1, 2). We describe the corresponding Klein pairs and determine their Poincaré-invariant structures: a carrollian structure on Ti, a pseudo-carrollian structure on Spi and a “doubly-carrollian” structure on Ni. We give additional geometric characterisations of these spaces as grassmannians of affine hyperplanes in Minkowski spacetime: Spi is the (double cover of the) grassmannian of affine lorentzian hyperplanes; Ti is the grassmannian of affine spacelike hyperplanes and Ni fibers over the grassmannian of affine null planes, which is   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$ . We exhibit Ni as the fibred product of   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  and the lightcone over the celestial sphere. We also show that Ni is the total space of the bundle of scales of the conformal carrollian structure on   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  and show that the symmetry algebra of its doubly-carrollian structure is isomorphic to the symmetry algebra of the conformal carrollian structure on   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$ ; that is, the BMS algebra. We show how to reconstruct Minkowski spacetime from any of its asymptotic geometries, by establishing that points in Minkowski spacetime parametrise certain lightcone cuts in the asymptotic geometries. We include an appendix comparing with (A)dS and observe that the de Sitter groups have no homogeneous spaces which could play the rôle that the celestial sphere plays in flat space holography.