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Jacobi-Lie T-plurality

by Jose J. Fernandez-Melgarejo, Yuho Sakatani

Submission summary

Authors (as registered SciPost users):

Jose J. Fernandez-Melgarejo

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 ${\cal L}_{E_A}E_B = - X_{AB}{}^C\,E_C$\,, where $X_{AB}{}^C$ are the structure constants of the DD$^+$ and ${\cal L}$ 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.