Are all the asymptotic symmetries always infinite dimensional?

Question

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!

Ali Seraj · Answer

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

Answered by Ali Seraj on June 8, 2021

Are all the asymptotic symmetries always infinite dimensional?

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