Pohlmeyer reduction revisited

Abstract

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

References in corpus (8)

• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Generating AdS String Solutions
• On reduced models for superstrings on AdS_n x S^n
• Solitons and AdS String Solutions
• Interacting finite-size magnons
• A note on the reduction of the AdS4 x CP3 string sigma model
• Toda equations associated with loop groups of complex classical Lie groups
• Lorentzian symmetric spaces in supergravity

Cited by in corpus (7)

• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Moduli Dynamics of AdS_3 Strings
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• A New and Elementary CP^n Dyonic Magnon
• A note on the reduction of the AdS4 x CP3 string sigma model
• Giant Magnons on CP^3 by Dressing Method