The conformal brane-scan: an update

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 vertical bar 4) N = 8, 4, 2, 1; SU(2, 2 vertical bar N) N = 4, 2, 1; F-2(4); OSp(8*vertical bar N), N = 4, 2. This correctly predicted the D3-brane with SU(2, 2 vertical bar 4) on AdS(5) x S-5 and the M5-brane with OSp(8*vertical bar 4) on AdS(7) x S-4, in addition to the known M2-brane with OSp(8 vertical bar 4) on AdS(4) x 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 vertical bar 3), OSp(3 vertical bar 4), OSp(5 vertical bar 4) and OSp(6 vertical bar 4) but not OSp(7 vertical bar 4). We also examine the status of p = (0, 1) configurations.

Automated summary

This article summarizes the research on BPS p-brane configurations and corresponding CFTs. The initial study was based on a 1987 paper, which proposed various membrane configurations with symmetries appearing on the boundary of anti-de Sitter space. Through a literature search, the authors confirmed that all the empty slots in the research on these configurations have now been filled.