Constants of Motion and the Conformal Anti-De Sitter Algebra in (2+1)-Dimensional Gravity

Abstract

Constants of motion are calculated for (2+1)-dimensional gravity with topology ℝ×T2 and negative cosmological constant. Certain linear combinations of them satisfy the anti-de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantization is straightforward in terms of the holonomy parameters. On inclusion of the Hamiltonian, three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2,3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.