Notes on the BMS group in three dimensions: II. Coadjoint representation

@article{Barnich2015NotesOT,
  title={Notes on the BMS group in three dimensions: II. Coadjoint representation},
  author={Glenn Barnich and Blagoje Oblak},
  journal={Journal of High Energy Physics},
  year={2015},
  volume={2015},
  pages={1-18}
}
A bstractThe coadjoint representation of the BMS3 group, which governs the covariant phase space of three-dimensional asymptotically flat gravity, is investigated. In particular, we classify coadjoint BMS3 orbits and show that intrinsic angular momentum is free of supertranslation ambiguities. Finally, we discuss the link with induced representations upon geometric quantization. 

Notes on the BMS group in three dimensions: I. Induced representations

A bstractThe Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the

Coadjoint representation of the BMS group on celestial Riemann surfaces

Abstract The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out

Characters of the BMS Group in Three Dimensions

Using the Frobenius formula, we evaluate characters associated with certain induced representations of the centrally extended BMS3 group. This computation involves a functional integral over a

BMS Modules in Three Dimensions

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an

Geometric actions for three-dimensional gravity

The solution space of three-dimensional asymptotically anti-de Sitter or flat Einstein gravity is given by the coadjoint representation of two copies of the Virasoro group in the former and the

Coadjoint Orbits of the Poincaré Group for Discrete-Spin Particles in Any Dimension

Considering the Poincaré group ISO(d−1,1) in any dimension d>3, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how

Holographic positive energy theorems in three-dimensional gravity

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the

Asymptotically flat spacetimes with BMS3 symmetry

We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The

On the Various Extensions of the BMS Group

The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry group of radiating asymptotically flat spacetimes. It has recently received renewed interest in the context of the flat

Coadjoint Orbits and Geometric Quantization

TLDR
This chapter is to describe the opposite phenomenon: starting from a coadjoint orbit of a group G, the orbit will obtain a representation by quantizing the orbit, which will further explain why orbits of momenta classify representations of semi-direct products.
...

References

SHOWING 1-10 OF 61 REFERENCES

Notes on the BMS group in three dimensions: I. Induced representations

A bstractThe Bondi-Metzner-Sachs group in three dimensions is the symmetry group of asymptotically flat three-dimensional spacetimes. It is the semi-direct product of the diffeomorphism group of the

Holographic positive energy theorems in three-dimensional gravity

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the

Relativistic field theories in three dimensions

We provide a complete classification of the unitary irreducible representations of the (2+1)‐dimensional Poincare group. We show, in particular, that only two types of ’’spin’’ are available for

Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity

A bstractStarting from the Chern-Simons formulation, the two-dimensional dual theory for three-dimensional asymptotically flat Einstein gravity at null infinity is constructed. Solving the

Quantization of conical spaces in 3D gravity

A bstractWe discuss the quantization and holographic aspects of a class of conical spaces in 2+1 dimensional pure AdS gravity. These appear as topological solitons in the Chern-Simons formulation of

Three-dimensional quantum geometry and black holes

We review some aspects of three-dimensional quantum gravity with emphasis in the ‘CFT → Geometry’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical

Virasoro Orbits, AdS_3 Quantum Gravity and Entropy

We analyse the canonical structure of AdS 3 gravity in terms of the coadjoint orbits of the Virasoro group. There is one subset of orbits, associated to BTZ black hole solutions, that can be

Classification of boundary gravitons in AdS3 gravity

A bstractWe revisit the description of the space of asymptotically AdS3 solutions of pure gravity in three dimensions with a negative cosmological constant as a collection of coadjoint orbits of the

Virasoro orbits, AdS3 quantum gravity and entropy

We analyse the canonical structure of AdS3 gravity in terms of the coadjoint orbits of the Virasoro group. There is one subset of orbits, associated to BTZ black hole solutions, that can be described

On the breakdown of asymptotic Poincare invariance in D = 3 Einstein gravity

The fact that neither momentum nor boosts are definable for finite energy solutions of Einstein gravity in D=3 is illustrated by contrasting the effect of Lorentz transformations on the corresponding
...