Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-08-25
JHEP 0810:087,2008
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, LaTeX, more references added, accepted for publication in JHEP
Scientific paper
10.1088/1126-6708/2008/10/087
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.
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