AdS2n spaces from SO(2n - 1, 2) instantons

Conformally invariant sigma models in D = 2n dimensions with target non-compact SO(2n, 1) groups are reviewed. Despite the non-compact nature of the SO(2n, 1), the classical action and Hamiltonian are positive definite. Instanton field configurations obeying a double self-duality condition are found to correspond geometrically to conformal stereographic mappings of R2n into the Euclidean signature AdS2n spaces. The direct link among generalized Yang–Mills systems, double-self-dual generalized Einstein–Cartan backgrounds, AdS2n spaces and p-branes, when d = p + 1 = 2n = 4k is established.