Classical solutions of sigma models in curved backgrounds by the Poisson-Lie T-plurality

Abstract

Classical equations of motion for three-dimensional sigma-models in curved background are solved by a transformation that follows from the Poisson-Lie T-plurality and transform them into the equations in the flat background. Transformations of coordinates that make the metric constant are found and used for solving the flat model. The Poisson-Lie transformation is explicitly performed by solving the PDE's for auxiliary functions and finding the relevant transformation of coordinates in the Drinfel'd double. String conditions for the solutions are preserved by the Poisson-Lie transformations. Therefore we are able to specify the type of sigma-model solutions that solve also equations of motion of three dimensional relativistic strings in the curved backgrounds. Simple examples are given.

References in corpus (4)

• Dual Non-Abelian Duality and the Drinfeld Double
• Poisson-Lie T-duality
• Classification of 6-dimensional real Drinfeld doubles
• Classical solution of a sigma-model in curved background

Cited by in corpus (5)

• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Non-Abelian U-duality for membrane
• On the Poisson-Lie T-plurality of boundary conditions
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality