Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle

Abstract

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string effective actions, the situation becomes more complicated due to the presence of the dilaton field. A novel approach to this problem using Levi-Civita connections on Courant algebroids is presented. After the introduction of necessary geometrical tools, formulas for the Poisson-Lie T-dual dilaton fields are derived. This provides a version of Poisson-Lie T-duality for string effective actions.

arXiv commentOne subsection added, several typos and minor mistakes corrected

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• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras