A comment on masses, quantum affine symmetries and PP-wave backgrounds

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) · Uq(hat-(Sl(2))) the N=2 piece is associated with the string conformal invariance and the Uq(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. (author)