On generalizations of asymptotically AdS_3 spaces and geometry of SL(N)
Abstract
In three and two dimensions the asymptotic symmetry groups of
AdS
spaces are infinite dimensional. This can be explained easily by noting the relations
Ad
S
3
≃SL(2)
and
Ad
S
2
≃SL(2)/SO(2)
, i.e. that the asymptotic symmetries are in fact that of the Lie group SL(2). As show in the author's previous work, similar infinite dimensional asymptotic symmetry groups can be found in the case of SL(3) and probably also for other noncompact Lie groups and their homogeneous spaces. The purpose of the present work is to revisit the
Ad
S
3
space in detail from the Lie group point of view by finding the boundary theory energy-momentum tensor and to prepare to tackle the SL(3) and SL(N) cases.