Supersymmetric field theories on AdS p × S q

Abstract

Abstract: In this paper we study supersymmetric field theories on an AdSp × Sq spacetime that preserves their full supersymmetry. This is an interesting example of supersymmetry on a non-compact curved space. The supersymmetry algebra on such a space is a (p − 1)-dimensional superconformal algebra, and we classify all possible algebras that can arise for p ≥ 3. In some AdS3 cases more than one superconformal algebra can arise from the same field theory. We discuss in detail the special case of four dimensional field theories with (Formula presented.) and (Formula presented.) supersymmetry on AdS3 × S1.