Quantum Anti-de Sitter space and sphere at roots of unity

Abstract

An algebra of functions on q-deformed Anti-de Sitter space AdS_q^D is defined which is covariant under U_q(so(2,D-1)), for q a root of unity. The star-structure is studied in detail. The scalar fields have an intrinsic high-energy cutoff, and arise most naturally as fields on orbifolds AdS_q^D \times S^D/G if D is odd, and AdS_q^D \times S_χ^{2D-1}/G if D is even. Here G is a finite abelian group, and S_χ is a certain ``chiral sector'' of the classical sphere. Hilbert spaces of square integrable functions are discussed. Analogous results are found for the q-deformed sphere S_q^D.

arXiv comment45 pages, LaTeX, 2 figures using epsf. Slight change in notation allows to obtain AdS^2, AdS^3 as special cases of the general scheme

References in corpus (8)

• AdS3 Black Holes and a Stringy Exclusion Principle
• 4d Conformal Field Theories and Strings on Orbifolds
• Towards Finite Quantum Field Theory in Non-Commutative Geometry
• Quantum Anti-de Sitter Space
• Quantum Groups, Roots of Unity and Particles on quantized Anti-de Sitter Space
• Gauge Fields and Singletons of $Ad{S}_{2p+1}$
• Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity
• Quantum Anti-de Sitter space and sphere at roots of unity

Cited by in corpus (3)

• Noncommutative spheres and the AdS/CFT correspondence
• Hidden classical symmetry in quantum spaces at roots of unity : From q-sphere to fuzzy sphere
• Quantum Anti-de Sitter space and sphere at roots of unity