Pohlmeyer reduction revisited

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 x M. In contrast, if M is of indefinite signature the solutions to those equations can describe bosonic string configurations on R-t x M, M x S-v(1). 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 CPn and AdS(n) are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.