Quotients of anti - de Sitter space

We study the quotients of n + 1-dimensional anti-de Sitter space by oneparameter subgroups of its isometry group SO(2, n) for general n. We classify the different quotients up to conjugation by O(2, n). We find that the majority of the classes exist for all n ≥ 2. There are two special classes which appear in higher dimensions: one for n ≥ 3 and one for n ≥ 4. The description of the quotient in the majority of cases is thus a simple generalisation of the AdS3 quotients. The study of the propagation of strings on more general curved backgrounds is important both because it allows us to confront some of the important problems arising in any theory of quantum gravity (such as the problem of time), and because describing strings on time-dependent backgrounds is essential to address the phenomenological application of string theory to cosmology. A new class of simple supersymmetric backgrounds referred to as null branes was recently constructed [1], by considering a novel class of Kaluza-Klein reductions of flat space. These do not have a timelike Killing field, so they provide interesting examples for studying string theory on more general backgrounds; in addition, a subclass of ‘parabolic orbifolds’ have initial singularities. String theory on these backgrounds has been intensively studied, to expand our understanding of string theory in non-static backgrounds and to attempt to gain insight into the resolution of such spacetime singularities in string theory [2, 3, 4]. Unfortunately, unlike in more familiar spacelike orbifolds, it turns out that the singular geometries suffer from an instability, so the resolution of the singularities is not accessible in perturbation theory [5, 3, 4, 6]. It is natural for many reasons to wish to extend these investigations to consider strings on orbifolds of Anti-de Sitter space (AdS). First, AdS is also a maximally symmetric space, so it has a large isometry group which can lead to interesting examples of quotients. Secondly, the AdS/CFT correspondence [7, 8] provides a non-perturbative definition of string theory, which may enable us to obtain more insight into issues such as singularity resolution in an AdS context. Finally, it is well-known that a [email protected] [email protected]