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.
Highlights
Lie bialgebras [25] are algebraic structures of Poisson– Lie groups [26], which play an important role in the theory of classical integrable systems
They play an important role in N = (2, 2) and N = (4, 4) supersymmetric WZW models [28,29,30]
In Ref. [31] we have studied the algebraic structure of N = (2, 2) and N = (4, 4) supersymmetric WZW models in more detail
Summary
Lie bialgebras [25] are algebraic structures of Poisson– Lie groups [26], which play an important role in the theory of classical integrable systems (see [27] for a review) They play an important role in N = (2, 2) and N = (4, 4) supersymmetric WZW models [28,29,30]. If the space-time coordinates were algebraic indices (like space-time coordinates, i.e., scalar and fermion fields in the BLG model) the B-field of the N = (4, 4) WZW model could be obtained from this form. 4 we express BLG model (M2model) on the Manin triple of that 3-Lie bialgebra and show that it turns into Yang–Mills and N = (4, 4) WZW model (D2-model) In this manner we show that using the correspondence of the 3-Lie bialgebra and Lie bialgebra one can construct M2-model from D2 and vice versa.
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