# Are all the asymptotic symmetries always infinite dimensional?

We know that the asymptotic symmetry of AdS$_3$ is the Virasoro symmetry, which is infinite dimensional. For flat spacetimes, the BMS group is also infinite dimensional. So are all the asymptotic symmetries always infinite dimensional? Can someone point out some reference that talks about this? Thank you!

• It's not a stupid question. – JamalS Oct 21 '17 at 1:07

This is not the case. For example, the asymptotic symmetries of asymptotically d+1 dimensional AdS spacetime with standard Dirichlet boundary conditions for $$d\geq 3$$ form the $$SO(d,2)$$ group which is finite dimensional. In general the asymptotic symmetry group strongly depends on the boundary conditions imposed.