  When two-dimensional Anti-de Sitter space (AdS_2) is endowed with a
non-constant dilaton the origin of the central charge in the Virasoro algebra
generating the asymptotic symmetries of AdS_2 can be traced back to the
breaking of the SL(2,R) isometry group of AdS_2. We use this fact to clarify
some controversial results appeared in the literature about the value of the
central charge in these models.
