M5-brane Solution in ABJM Theory and Three-algebra

Understand

We construct a new classical solution in the ABJM theory corresponding to M5-branes with a non-zero self-dual three form flux.

• This is an M-theory lift of the D4-brane solution expressed as a non-commutative plane in the three dimensional super Yang-Mills theory.
• We discuss that our solution is closely related with the three-algebra.
• We show that the corresponding configuration of the M5-brane satisfies the equations of motion in the single M5-brane action.