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arXiv · hep-th/9910037

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

Harold Steinacker
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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.

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Harold Steinacker. 1999-10-10. Quantum Anti-de Sitter space and sphere at roots of unity. https://doi.org/10.1142/s0217979200002041

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