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

TL;DR

This paper extends the use of 3-Leibniz bialgebras to describe boundary conditions and dualities between M2-branes and D2-branes in N=6 Chern-Simons theories, generalizing previous N=8 results.

Contribution

It introduces the concept of 3-Leibniz bialgebras for N=6 BL models, broadening the algebraic framework beyond 3-Lie bialgebras, and explores their implications for brane boundary conditions and equations.

Findings

Reduction of Basu-Harvey to Nahm equations via Leibniz bialgebra correspondence

Connection of D2-brane boundary conditions to N=(4,4) WZW model with 2-cocycle

Generalization of boundary condition analysis from N=8 to N=6 supersymmetry

Abstract

Constructing M2-brane and its boundary conditions from D2-brane and the related boundary conditions and vice versa has been possible in our recent work by using 3-Lie bialgebra for BLG model with N = 8 supersymmetry. This could be generalized for BL model with N = 6 by the concept of the 3-Leibniz bialgebra. The 3-Lie bialgebra is an especial case of 3-Leibniz bialgebra, then more comprehensive information will be obtained in this work. Consequently, according to the correspondence of these 3-Leibniz bialgebras with Lie bialgebras, we reduce to D2-brane such that with some restrictions on the gauge field this D2-brane is related to the bosonic sector of an N = (4,4) WZW model equipped with one 2-cocycle in its Lie bialgebra structure. Moreover, the Basu-Harvey equation which is found by considering boundary conditions for BL model containing Leibniz bialgebra structure is reduced to Nahm equation and vice versa using this correspondence.