Pohlmeyer reduction revisited
Abstract
Description
A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with target-space a symmetric space M=F/G and a class of integrable multi-component generalizations of the sine-Gordon equation. When M is of definite signature their solutions describe classical bosonic string configurations on the curved space-time R_t\times M. In contrast, if M is of indefinite signature the solutions to those equations can describe bosonic string configurations on R_t\times M, M\times S^1_\vartheta or simply M. The conditions required to enable the Lagrangian formulation of the resulting equations in terms of gauged WZW actions with a potential term are clarified, and it is shown that the corresponding Lagrangian action is not unique in general. The Pohlmeyer reductions of sigma models on CP^n and AdS_n are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.
45 pages, LaTeX, more references added, accepted for publication in JHEP
45 pages, LaTeX, more references added, accepted for publication in JHEP