The conformal brane-scan: an update

A bstract Generalizing the The Membrane at the End of the Universe , a 1987 paper Supersingletons by Blencowe and the author conjectured the existence of BPS p -brane configurations ( p = 2 , 3 , 4 , 5) and corresponding CFTs on the boundary of anti-de Sitter space with symmetries appearing in Nahm’s classification of superconformal algebras: OSp( N| 4) N = 8, 4, 2, 1; SU(2, 2 |N ) N = 4, 2, 1; F 2 (4); OSp(8 ∗ |N ), N = 4, 2. This correctly predicted the D 3-brane with SU(2, 2 | 4) on AdS 5 × S 5 and the M 5-brane with OSp(8 ∗ | 4) on AdS 7 × S 4 , in addition to the known M 2-brane with OSp(8 | 4) on AdS 4 × S 7 . However, finding non-singular AdS solutions matching the other symmetries was less straightforward. Here we perform a literature search and confirm that all of the empty slots have now been filled, thanks to a number of extra ingredients including warped products and massive Type IIA. Orbifolds, orientifolds and S-folds also play a part providing examples not predicted: SU(2, 2 | 3), OSp(3 | 4), OSp(5 | 4) and OSp(6 | 4) but not OSp(7 | 4). We also examine the status of p = (0, 1) configurations.