Jacobi-Lie T-plurality

Abstract

We propose a Leibniz algebra, to be called DD${}^{+}$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD${}^{+}$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfel'd double. We then construct generalized frame fields $E_A{}^M\in \text{O}(D,D)\times {\mathbb{R}}^{+}$ satisfying the algebra ${\mathcal{L}}_{E_A}{E}_B=-X_{AB}{}^C{E}_C$, where $X_{AB}{}^C$ are the structure constants of the DD${}^{+}$ and $\mathcal{L}$ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi-Lie T-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi-Lie T-plurality with or without Ramond-Ramond fields and the spectator fields.

30 pages; v2: minor corrections, references added; v3 matches the published version: extended the discussion, an appendix and references added