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 = F/G and a class of integrable multi-component generalizations of the sine-Gordon equation. When is of definite signature their solutions describe classical bosonic string configurations on the curved space-time _t × . In contrast, if is of indefinite signature the solutions to those equations can describe bosonic string configurations on _t × , × S¹_ϑ or simply . 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 Pⁿ and AdS_n are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.