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

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 N= (4 , 4) 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.