Eur. Phys. J. C (2016) 76: 632
https://doi.org/10.1140/epjc/s10052-016-4477-y

Regular Article - Theoretical Physics

M2 to D2 and vice versa by 3-Lie and Lie bialgebra

Department of Physics, Faculty of science, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran

^* e-mail: aali@azaruniv.edu

Received: 30 August 2016
Accepted: 1 November 2016
Published online: 19 November 2016

Abstract

Using the concept of a 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct a Bagger–Lambert–Gustavson (BLG) model for the M2-brane on a Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and the relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an WZW model (D2-brane), such that its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using the correspondence of the 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct the M2-brane from a D2-brane and vice versa.