  We show that the symmetries of effective D-string actions in constant dilaton
backgrounds are directly related to homothetic motions of the background
metric. In presence of such motions, there are infinitely many nonlinearly
realized rigid symmetries forming a loop (or loop like) algebra. Near horizon
(AdS) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2d
interacting field theories with infinite conformal symmetry.
