Quotients of anti-de Sitter space

TL;DR

This paper classifies various quotient spaces of anti-de Sitter space by one-parameter isometry subgroups across different dimensions, revealing new classes in higher dimensions and generalizing known lower-dimensional cases.

Contribution

It provides a comprehensive classification of AdS space quotients for all dimensions n ≥ 2, including the discovery of new classes in higher dimensions.

Findings

Most quotient classes exist for all n ≥ 2

Two special classes appear in higher dimensions (n ≥ 3 and n ≥ 4)

Descriptions of quotients generalize AdS_3 cases

Abstract

We study the quotients of n+1-dimensional anti-de Sitter space by one-parameter 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 \geq 2. There are two special classes which appear in higher dimensions: one for n \geq 3 and one for n \geq 4. The description of the quotient in the majority of cases is thus a simple generalisation of the AdS_3 quotients.