From Basu-Harvey to Nahm equation via 3-Lie bialgebra

Abstract

Using the concept of 3-Lie bialgebra; we construct the Bagger- Lambert- Gustavson (BLG) model on the Manin triple $\mathcal{D}$ of the especial 3-Lie bialgebra $(\mathcal{D},{\mathcal{A}}_{\mathcal{G}},{\mathcal{A}}_{{\mathcal{G}}^{\ast }}^{\ast })$ which is in correspondence with Manin triple of Lie bialgebra $(\mathcal{D},\mathcal{G},{\mathcal{G}}^{\ast })$. We have shown that the Nahm equation (with Lie bialgebra $\mathcal{G}$) can be obtained from the Basu-Harvey equation as a boundary condition of BLG model (with 3-Lie bialgebra $\mathcal{D}$) and vice versa.

7 pages. Two references are added

References in corpus (8)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Comments on the Bagger-Lambert theory and multiple M2-branes
• On M5-branes in N=6 Membrane Action
• Boundary Conditions for Interacting Membranes
• From N M2's to N D2's
• 3-Leibniz bialgebras (3-Lie bialgebras)

Cited by in corpus (2)

• M2 to D2 and vice versa by 3-Lie and Lie bialgebra
• 3-Leibniz bialgebra in $N=6$ Chern-Simons gauge theories, multiple M2 to D2 branes and vice versa