  We discuss string theory on AdS(3)xS(3)xM(4) with particular emphasis on
unitarity and state-operator correspondence. The AdS-CFT correspondence, in the
Minkowski signature, is re-examined by taking into account the only allowed
unitary representation: the principal series module of the affine current
algebra SL(2,R) supplemented with zero modes. Zero modes play an important role
in the description of on-shell states as well as of windings in space-time at
the AdS(3) boundary. The theory is presented as part of the supersymmetric WZW
model that includes the supergroup SU(2/1,1) or OSp(4/2) or D(2,1;\alpha) with
central extension k. A free field representation is given and the vertex
operators are constructed in terms of free fields in SL(2,R) principal series
representation bases that are labeled by position space or momentum space at
the boundary of AdS(3). The vertex operators have the correct operator products
with the currents and stress tensor, all of which are constructed from free
fields, including the subtle zero modes. It is shown that as k goes to
infinity, AdS(3) tends to flat 3D-Minkowski space and the AdS(3) vertex
operators in momentum space tend to the vertex operators of flat 3D-string
theory (furthermore the theory readjusts smoothly in the rest of the dimensions
in this limit).
