3-dimensional $\Lambda$-BMS Symmetry and its Deformations

Abstract

In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible Lie bialgebra structures and for selected examples, we explicitly construct the related Hopf algebras. Using cohomological arguments we show that this construction can always be performed by a so-called twist deformation. The resulting structures can be compared to the well-known $\kappa$-Poincaré Hopf algebras constructed on the finite dimensional Poincaré or (anti) de Sitter algebra. The dual $\kappa$ Minkowski spacetime is supposed to describe a specific non-commutative geometry. Importantly, we find that some incarnations of the $\kappa$-Poincaré can not be extended consistently to the infinite dimensional algebras. Furthermore, certain deformations can have potential physical applications if subalgebras are considered. Since the conserved charges associated with asymptotic symmetries in 3-dimensional form a centrally extended algebra we also discuss briefly deformations of such algebras. The presence of the full symmetry algebra might have observable consequences that could be used to rule out these deformations. }

arXiv comment38 pages, revised and extended version, matching JHEP publication. New section discusses centrally extended algebra

References in corpus (25)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Asymptotic symmetries and subleading soft graviton theorem
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• Symplectic structures associated to Lie-Poisson groups
• New Boundary Conditions for AdS3
• Soft Heisenberg hair on black holes in three dimensions
• Spacetime structure near generic horizons and soft hair
• Symplectic structure of the moduli space of flat connections on a Riemann surface
• BMS Particles in Three Dimensions
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Centrally extended BMS4 Lie algebroid
• Reconstructing AdS/CFT
• Symmetries of quantum space-time in 3 dimensions
• Lectures on black holes and the AdS_3 / CFT_2 correspondence
• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• The (super)conformal BMS${}_3$ algebra
• Quantum deformations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries in unified $\mathfrak{o}(4;\mathbb{C})$ setting -- Addendum
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• A canonical realization of the Weyl BMS symmetry
• $\kappa$-deformed BMS symmetry