Conformally invariant supersymmetric field theories on Sp S1 and super p-branes
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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) {circled asterisk operator} 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. 1988.