Promoting finite to infinite symmetries: the 3+1-dimensional analogue of the Virasoro algebra and higher-spin fields
arXiv:hep-th/0002109 · doi:10.1142/S0217732300000943
Abstract
Infinite enlargements of finite pseudo-unitary symmetries are explicitly provided in this letter. The particular case of u(2,2)=so(4,2)+u(1) constitutes a (Virasoro-like) infinite-dimensional generalization of the 3+1-dimensional conformal symmetry, in addition to matter fields with all conformal spins. These algebras provide a new arena for integrable field models in higher dimensions; for example, Anti-de Sitter and conformal gauge theories of higher-so(4,2)-spin fields. A proposal for a non-commutative geometrical interpretation of space is also outlined.
7 pages, latex, no figures; note and reference added; to appear in Mod. Phys. Lett. A