  The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a
q-deformation that relates it to the S-matrix of a generalization of the
sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring.
Whilst this is a fascinating development the resulting S-matrix is not
explicitly unitary. The problem has been known for a long time in the context
of S-matrices related to quantum groups. A braiding relation often called
"unitarity" actually only corresponds to quantum field theory unitarity when
the S-matrix is Hermitian analytic and quantum group S-matrices manifestly
violate this. On the other hand, overall consistency of the S-matrix under the
bootstrap requires that the deformation parameter is a root of unity and
consequently one is forced to perform the "vertex" to IRF, or SOS,
transformation on the states to truncate the spectrum consistently. In the IRF
formulation unitarity is now manifest and the string S-matrix and the S-matrix
of the generalised sine-Gordon theory are recovered in two different limits. In
the latter case, expanding the Yang-Baxter equation we find that the tree-level
S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical
Yang-Baxter equation explaining the apparent anomaly in the perturbative
computation. We show that the IRF form of the S-matrix meshes perfectly with
the bootstrap equations.
