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

TL;DR

This paper constructs a theoretical framework linking M2-branes and D2-branes via 3-Lie and Lie bialgebras, providing a new algebraic approach to relate these branes in string theory.

Contribution

It introduces a novel method to derive M2-brane models from D2-brane models using 3-Lie and Lie bialgebra structures, expanding the algebraic tools in brane theory.

Findings

Constructed BLG model for M2-brane using 3-Lie bialgebra

Reduced M2-brane model to an N=(4,4) WZW model for D2-brane

Established algebraic correspondence between 3-Lie bialgebra 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 the 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.