On Generalizations of Asymptotically AdS3 Spaces and Geometry of SL(N)

摘要

In three and two dimensions the asymptotic symmetry groups of AdS spaces areinfinite dimensional. This can be explained easily by noting the relations AdS3 SL(2) andAdS2 SL(2)/SO(2), i.e. that the asymptotic symmetries are in fact that of the Lie groupSL(2). As show in the author’s previous work, similar infinite dimensional asymptotic symmetrygroups can be found in the case of SL(3) and probably also for other noncompact Lie groupsand their homogeneous spaces. The purpose of the present work is to revisit the AdS3 spacein detail from the Lie group point of view by finding the boundary theory energy-momentumtensor and to prepare to tackle the SL(3) and SL(N) cases.