Quantum double and κ-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory
نویسنده
چکیده
We review the role of Drinfeld doubles and κ-Poincaré symmetries in quantised (2+1)gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we explain that the usual κ-Poincaré symmetries with a timelike deformation are not directly associated with (2+1)-gravity. These κ-Poincaré symmetries are linked to Chern-Simons theory only in the de Sitter case, and the relevant Chern-Simons theory is physically inequivalent to (2+1)-gravity. PACS numbers: 04.20.Cv, 02.20.Qs, 02.40.-k
منابع مشابه
Generalised Chern-Simons actions for 3d gravity and κ-Poincaré symmetry
We consider Chern-Simons theories for the Poincaré, de Sitter and anti-de Sitter groups in three dimensions which generalise the Chern-Simons formulation of 3d gravity. We determine conditions under which κ-Poincaré symmetry and its de Sitter and anti-de Sitter analogues can be associated to these theories as quantised symmetries. Assuming the usual form of those symmetries, with a timelike vec...
متن کاملMagnetic Symmetries and Vortices In Chern-Simons Theories
We study the locality properties of the vortex operators in compact U(1) MaxwellChern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically ...
متن کاملA Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
We define and discuss classical and quantum gravity in 2+1 dimensions in the Galilean limit. Although there are no Newtonian forces between massive objects in (2+1)dimensional gravity, the Galilean limit is not trivial. Depending on the topology of spacetime there are typically finitely many topological degrees of freedom as well as topological interactions of Aharonov-Bohm type between massive...
متن کاملW∞ and SLq(2) Algebras in the Landau Problem and Chern-Simons Theory on a Torus
We discuss w∞ and slq(2) symmetries in Chern-Simons theory and Landau problem on a torus. It is shown that when the coefficient of the ChernSimons term, or when the total flux passing through the torus is a rational number, there exist in general two w∞ and two slq(2) algebras, instead of one set each discussed in the literature. The general wavefunctions for the Landau problem with rational to...
متن کاملLagrangian Symmetries of Chern–simons Theories
This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension d = 3. In particular, we find an expression for the superpotential of ChernSimons gravity. As a by-product the general discussion of superpotentials for 3rd order natural and quasi-natural theories is also given. PACS number(s): 04.20.Fy, 11.10Kk, 11.30.-j, 04.20.Cv
متن کامل