Promoting finite to infinite symmetries: the 3 + 1-dimensional analogue of the Virasoro algebra and higher-spin fields

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) infinitedimensional 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.