  Two dimensional light cone world sheet massive models can be used to define
good string backgrounds.In many cases these light cone world sheet lagrangians
flow from a CFT in the UV to a theory of massive particles in the IR. The
relevant symmetry in the IR, playing a similar role to Virasoro in the UV, are
quantum affine Kac Moody algebras. Finite dimensional irreps of this algebra
are associated with the spectrum of massive particles. The case of N=0 Sine
Gordon at the N=2 point is associated with a Landau Ginzburg model that defines
a good string background. For the world sheet symmetry $(N=2) \otimes
U_{q}(\hat{Sl(2)})$ the N=2 piece is associated with the string conformal
invariance and the $U_{q}(\hat{Sl(2)})$ piece with the world sheet RG. The two
dimensional light cone world sheet massive model can be promoted to a CFT by
adding extra light cone fields $X^{-}$ and $X^{+}$. From the point of view of
the quantum affine symmetry these two fields are associated, respectively, with
the center and the derivation of the affine Kac Moody algebra.
