Jacobi-Lie T-plurality

Fernandez-Melgarejo, Jose J.; Sakatani, Yuho

doi:10.21468/SciPostPhys.11.2.038

SciPost Physics

Jacobi-Lie T-plurality

Jose J. Fernandez-Melgarejo, Yuho Sakatani

SciPost Phys. 11, 038 (2021) · published 23 August 2021

doi: 10.21468/SciPostPhys.11.2.038
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.2.038
TI  - Jacobi-Lie T-plurality
PY  - 2021/08/23
UR  - https://scipost.org/SciPostPhys.11.2.038
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 2
SP  - 038
A1  - Fernandez-Melgarejo, Jose J.
AU  - Sakatani, Yuho
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.11.2.038,
	title={{Jacobi-Lie T-plurality}},
	author={Jose J. Fernandez-Melgarejo and Yuho Sakatani},
	journal={SciPost Phys.},
	volume={11},
	pages={038},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.2.038},
	url={https://scipost.org/10.21468/SciPostPhys.11.2.038},
}

Cited by 5

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¹ Jose J. Fernandez-Melgarejo,
² Yuho Sakatani

Funders for the research work leading to this publication

日本学術振興会 / Japan Society for the Promotion of Science [JSPS]
Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])