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

Abstract

Using the concept of 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using of correspondence and 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 correspondence of 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.

3-Leibniz bialgebras (3-Lie bialgebras)

“…The definition of r-matrix and Yang-Baxter equation were related to 3-Leibniz and 3-Lie bialgebra. Applying the definition of 3-Lie bialgebra in M theory [10,11,12] as a physical application is our future [22]. We know that for the Nambu-Lie group G [23] on the dual space g * of the Lie algebra g we have an n-Lie algebra structure.…”