AdS3 vacua realising osp $$ \mathfrak{osp} $$ (n|2) superconformal symmetry

Abstract

Abstract We consider N $$ \mathcal{N} $$ = (n, 0) supersymmetric AdS3 vacua of type II supergravity realising the superconformal algebra osp $$ \mathfrak{osp} $$ (n|2) for n > 4. For the cases n = 6 and n = 5, one can realise these algebras on backgrounds that decompose as foliations of AdS3 × ℂℙ3 ( squashed ℂℙ3 for n = 5) over an interval. We classify such solutions with bi-spinor techniques and find the local form of each of them: they only exist in (massive) IIA and are defined locally in terms of an order 3 polynomial h similar to the AdS7 vacua of (massive) IIA. Many distinct local solutions exist for different tunings of h that give rise to bounded (or semi infinite) intervals bounded by physical behaviour. We show that it is possible to glue these local solutions together by placing D8 branes in the interior of the interval without breaking supersymmetry, which expands the possibilities for global solutions immensely. We illustrate this point with some simple examples. Finally we also show that AdS3 vacua for n = 7, 8 only exist in d = 11 supergravity and are all locally AdS4 ×S7.

Keywords

• Extended Supersymmetry
• Flux Compactifications
• Superstring Vacua
• AdS-CFT Correspondence