A Comment on Masses, Quantum Affine Symmetries and PP-Wave Backgrounds

TL;DR

This paper explores how two-dimensional light cone world sheet massive models relate to string backgrounds, emphasizing the role of quantum affine Kac-Moody symmetries in IR and UV regimes, and their connection to conformal invariance.

Contribution

It analyzes the connection between quantum affine symmetries and string backgrounds, highlighting the role of these symmetries in IR and UV limits of light cone world sheet models.

Findings

Quantum affine Kac-Moody algebras characterize IR symmetries.

N=2 Sine Gordon model defines a good string background.

Adding light cone fields promotes models to conformal field theories.

Abstract

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.