Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these lead to a surprisingly simple symmetry algebra consisting two affine u(1) current algebras. The is essentially equivalent Heisenberg algebra. associated charges give specific example "soft hair" on horizon, as defined by Hawking, Perry and Strominger. show soft hair does...

We explore the spacetime structure near non-extremal horizons in any dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by functional dynamical variables, describing inequivalent interactions at horizon with thermal bath. 2. The algebra set conditions, labeled parameter $s$, is given semi-direct sum diffeomorphisms "spin-$s$ supertranslations". For $s=1$ we obtain first explicit realization Bondi-Metzner-Sachs algebra. 3. another...

Three-dimensional spacetime with a negative cosmological constant has proven to be remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees freedom, asymptotic symmetries become all more crucial. For pure (2 + 1) they consist two copies Virasoro algebra. There exists black hole which may endowed corresponding charges. reformulated in terms Chern-Simons connections sl (2, $ \mathbb{R} ). This permits...

We discuss some aspects of soft hairy black holes and a new kind ``soft cosmologies,'' including detailed derivation the metric formulation, results on flat space, novel observations concerning entropy. Remarkably, like in case with negative cosmological constant, we find that asymptotic symmetries for locally spacetimes horizon are governed by infinite copies Heisenberg algebra generate hair descendants. It is also shown generators three-dimensional Bondi-Metzner-Sachs arise from composite...

It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by nonnegative integer $k$. Gravitational excitations are then described "boundary gravitons" fulfill the equations $k$-th element KdV hierarchy. In particular, $k=0$ corresponds to Brown-Henneaux so chiral movers. case $k=1$, gravitons equation and asymptotic symmetry algebra turns out be infinite-dimensional, abelian devoid central...

We explicitly establish the equivalence between magnetic Carrollian limit of Einstein gravity defined through Hamiltonian formalism and theory a gauging Carroll algebra along lines standard Poincar\'e (or (A)dS) gaugings.

We exploit the close relationship between Carroll and fracton/dipole algebras, together with method of coadjoint orbits, to define classify classical fracton particles. This approach establishes a Carroll/fracton correspondence provides an answer question "What is fracton?". Under this correspondence, carrollian energy center-of-mass correspond electric charge dipole moment, respectively. Then immobile massive particles monopoles, whereas certain mobile ("centrons") elementary dipoles....

A bstract We classify and relate unitary irreducible representations (UIRs) of the Carroll dipole groups, i.e., we define elementary quantum fracton particles establish a correspondence between them. Whenever possible, express UIRs in terms fields on Carroll/Aristotle spacetime subject to their free field equations. emphasise that massive (or “electric”) theories are ultralocal highlight peculiar puzzling thermodynamic features. also comment subtle differences massless “magnetic” discuss...

Despite the absence of a lightcone structure, some solutions Carroll gravity show black hole-like behaviour. We define holes as that exhibit thermal properties and have extremal surface, notions introduced in our work. The latter is analogue Lorentzian surface. As examples, we discuss versions Schwarzschild, Reissner-Nordström, BTZ hole generic 1+1 dimensional dilaton gravity, including JT Witten holes.

Chern-Simons models for gravity are interesting because they provide with a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been perceived remoteness from standard General Relativity, based on presence of higher powers curvature Lagrangian (except, remarkably, three-dimensional spacetime). Here we report simple model that suggests mechanism by which Relativity five-dimensional spacetime may indeed emerge at special critical point...

A bstract Asymptotic symmetries in Carrollian gravitational theories 3+1 space and time dimensions obtained from “magnetic” “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions needed to guarantee a finite symplectic term, analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim imposed, asymptotic described by Carroll group. With Henneaux-Troessaert conditions, symmetry algebra corresponds BMS-like extension...

A bstract Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant Λ are analyzed in 3+1 space-time dimensions. In the theory, asymptotic symmetry algebra is given by conformal Carroll three dimensions, which infinite-dimensional isomorphic to BMS 4 algebra. These results full agreement holographic expectations, providing new framework for study holography. On contrary, case presence turns out be incompatible consistent set...

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

It has been recently argued that the averaging of free CFT's over Narain lattice can be holographically described through a Chern-Simons theory for $U\left(1\right)^{D}\times U\left(1\right)^{D}$ with precise prescription to sum three-dimensional handlebodies. We show gravitational dual these averaged would provided by Einstein gravity on AdS$_{3}$ $U\left(1\right)^{D-1}\times U\left(1\right)^{D-1}$ gauge fields, endowed set boundary conditions closely related "soft hairy" ones....

We study gravitational radiation for a positive value of the cosmological constant $\mathrm{\ensuremath{\Lambda}}$. rely on two battle-tested procedures: (i) start from same null coordinate system used by Bondi and Sachs $\mathrm{\ensuremath{\Lambda}}=0$, but, introduce boundary conditions adapted to allow when $\mathrm{\ensuremath{\Lambda}}>0$; (ii) determine asymptotic symmetries studying, \`a la Regge-Teitelboim, surface integrals generated in action these conditions. A crucial difference...

A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components gauge fields that manifestly preserve original extension BMS3 algebra, with same central charge. By virtue a suitable permissible choice, it shown this can be directly recovered as limit boundary have been recently constructed case negative constant, whose symmetries are spanned by two copies...

We construct a new set of boundary conditions for higher spin gravity, inspired by recent "soft Heisenberg hair"-proposal General Relativity on three-dimensional Anti-de Sitter space. The asymptotic symmetry algebra consists affine û(1) current algebras. Its associated canonical charges generate soft hair. focus first the spin-3 case and then extend some our main results to spin-N , many which resemble spin-2 results: generators W 3 naturally emerge from composite operators through twisted...

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms Riemannian geometry locally flat spacetimes three dimensions. The analysis is performed two-dimensional gauge fields for $$ isl\left(2,\mathrm{\mathbb{R}}\right) , being isomorphic Poincaré algebra 3D. Although not semisimple, formulation can still be carried out à la Drinfeld-Sokolov because it admits nondegenerate invariant bilinear metric. turns...

We study dipole Chern-Simons theory with and without a cosmological constant in $2+1$ dimensions. write the second order formulation show that this leads to fracton gauge coupled Aristotelian geometry which can also be matter. This coupling exhibits remarkable property of generalizing invariance curved spacetimes, placing any limitations on possible geometries. use construct higher dimensional generalization action. Finally, for $(2+1)$-dimensional we find solutions interpret these as...

We revisit the classifications of classical and quantum galilean particles: that is, we fully classify homogeneous symplectic manifolds unitary irreducible projective representations Galilei group. Equivalently, these are coadjoint orbits Bargmann group, universal central extension provide an action principle in each case, discuss nonrelativistic limit, as well exhibit, whenever possible, terms fields on spacetime. Motivated by a forthcoming study planons pay close attention to mobility less...

The conformal extension of the BMS$_{3}$ algebra is constructed. Apart from an infinite number 'superdilatations,' in order to incorporate 'superspecial transformations,' commutator latter with supertranslations strictly requires presence nonlinear terms remaining generators. appears be very rigid, sense that its central extensions as well coefficients become determined by charge Virasoro subalgebra. wedge corresponds group three spacetime dimensions $SO(3,2)$, so full can also interpreted...

The expansion of a Lie algebra entails finding new, bigger G, through series well-defined steps, from an original g. One incarnation the method, so-called S-expansion, involves use finite abelian semigroup S to accomplish this task. In paper we put forward dual formulation S-expansion method which is based on picture given by Maurer-Cartan forms. version useful in generalization case gauge free differential algebra, turn relevant for physical applications in, e.g., Supergravity. It also...