# M5-brane Solution in ABJM Theory and Three-algebra

## TL;DR

This paper constructs a classical M5-brane solution within ABJM theory, revealing its relation to three-algebra structures and matching tensions with known M5-brane actions, advancing understanding of M-theory branes.

## Contribution

It introduces a novel M5-brane solution in ABJM theory with self-dual flux, linking it to three-algebra and verifying consistency with M5-brane tension calculations.

## Key findings

- Constructed M5-brane solution with self-dual flux in ABJM theory
- Demonstrated the solution satisfies M5-brane equations of motion
- Found tension matches with single M5-brane action

## Abstract

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. We find the agreement between the tension of the M5-brane solution in the ABJM action and the one computed from the single M5-brane action.