3-dimensional Λ-BMS symmetry and its deformations
TL;DR: In this article, the authors studied quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in 3-dimensional Lie bialgebra structures.
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 explicitely 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 κ-Poincare Hopf algebras constructed on the finite dimensional Poincare or (anti) de Sitter algebra. The dual κ Minkowski spacetime is supposed to describe a specific non-commutative geometry. Importantly, we find that some incarnations of the κ-Poincare 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.
References
More filters
TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.
Abstract: We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.
15,567 citations
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
Abstract: It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS
3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in 1+1 dimensions.
5,093 citations
TL;DR: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution that appears as a negative energy state separated by a mass gap from the continuous black hole spectrum.
Abstract: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole---characterized by mass, angular momentum, and charge, defined by flux integrals at infinity---is quite similar to its 3+1 counterpart. Anti--de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Evaluation of the partition function yields that the entropy is equal to twice the perimeter length of the horizon.
3,640 citations
TL;DR: In this article, it was shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level.
Abstract: It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.
3,072 citations
Book•
01 Jan 1994
TL;DR: In this paper, the Kac-Moody algebras and quasitriangular Hopf algesas were used to represent the universal R-matrix and the root of unity case.
Abstract: Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. Quasitriangular Hopf algebras 5. Representations and quasitensor categories 6. Quantization of Lie bialgebras 7. Quantized function algebras 8. Structure of QUE algebras: the universal R-matrix 9. Specializations of QUE algebras 10. Representations of QUE algebras: the generic case 11. Representations of QUE algebras: the root of unity case 12. Infinite-dimensional quantum groups 13. Quantum harmonic analysis 14. Canonical bases 15. Quantum group invariants of knots and 3-manifolds 16. Quasi-Hopf algebras and the Knizhnik-Zamolodchikov equation Appendix. The Kac-Moody algebras.
2,637 citations