The conformal brane-scan: an update - Duff,MJ (JOURNAL OF HIGH ENERGY PHYSICS, 2022)
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 D3-brane with SU(2, 2|4) on AdS5 × S5 and the M5-brane with OSp(8∗|4) on AdS7 × S4, in addition to the known M2-brane with OSp(8|4) on AdS4 × S7. 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.