Conformally invariant supersymmetric field theories on Sp × S1 and super p-branes

We construct supersymmetric field theories on Sp × S1 for p = 1,…,5. These spaces are the boundaries of the anti-de Sitter space in (p + 2)-dimensions. Thesetheories are invariant under the super extension of the anti-de Sitter group in (p + 2)-dimensions, whose bosonic subalgebra is SO(p + 1,2) asterisk in circle SO(N), for N = 1,2,4,8. The anti-de Sitter group SO(p + 1,2) acts as the conformal group on Sp × S1. We conjecture that these theories describe the super p-branes propagating in AdSp + 2 × SN−1. The internal space is always one of the parallelizable spheres, namely S1, S3 or S7