BMS Modules in Three Dimensions

Abstract

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 ultrarelativistic limit of highest-weight representations of Virasoro and W algebras, which is to be contrasted with non-relativistic limits that typically give non-unitary representations. To support this dichotomy, we also point out that the ultrarelativistic and non-relativistic limits of generic W algebras differ in the structure of their non-linear terms.

27 pages; contribution to the proceedings of the workshop "Higher Spin Gauge Theories", Institute for Advanced Studies, NTU, Singapore, November 4-6, 2015

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• Soft hairy horizons in three spacetime dimensions
• Flat space physics from AdS/CFT
• Geometric actions for three-dimensional gravity
• A Tale of Three. Tensionless strings and vacuum structure
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• A BMS-invariant free scalar model
• Tensionless Superstrings: View from the Worldsheet
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• The nuts and bolts of the BMS Bootstrap
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• The tensionless path from closed to open strings
• Geometric actions and flat space holography
• Symmetries of free massless particles and soft theorems
• Higher-Spin Flat Space Cosmologies with Soft Hair
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Massless Scalars and Higher-Spin BMS in Any Dimension
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• Semi-classical BMS${}_3$ blocks and flat holography
• Asymptotically flat spacetimes with BMS${}_3$ symmetry
• Spectral Flow in 3D Flat Spacetimes
• Free-field realisations of the BMS${}_3$ algebra and its extensions
• The complex null string, Galilean conformal algebra and scattering equations
• BMS Characters and Modular Invariance
• Gravitation in flat spacetime from entanglement
• Logarithmic Celestial Conformal Field Theory
• The Shadow Formalism of Galilean CFT${}_2$
• Galilean contractions of $W$-algebras
• Quantum BMS transformations in conformally flat space-times and holography
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• Linking Past and Future Null Infinity in Three Dimensions
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Enhanced asymptotic $BM{S}_3$ algebra of the flat spacetime solutions of generalized minimal massive gravity
• BMS symmetry, soft particles and memory
• Extended Supersymmetric BMS${}_3$ algebras and Their Free Field Realisations
• Asymptotic symmetries in spatially flat FRW
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• BMS Modular Diaries: Torus one-point function
• Quantization of Carrollian conformal scalar theories
• Higher-spin gauge theories in three spacetime dimensions
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Supersymmetric Galilean conformal blocks
• Semi-classical BMS-blocks from the Oscillator Construction
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Hypergravity in five dimensions
• Probing Wigner Rotations for Any Group
• Higher-order Galilean contractions
• Carroll spinors
• Multi-graded Galilean conformal algebras
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Universal sectors of two-dimensional Carrollian CFTs
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Free-field construction of Carrollian $W_N$-algebras
• Carrollian superconformal theories and super BMS