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We construct an action for non-abelian 2-form in 6-dimensions. Our actionconsists of a non-abelian generalization of the abelian action of Perry andSchwarz for a single five-brane. It admits a self-duality equation on the fieldstrength as the equation of motion. It has a modified 6d Lorentz symmetry. Ondimensional reduction on a circle, our action gives the standard 5d Yang-Millsaction plus higher order corrections. Based on these properties, we proposethat our theory describes the gauge sector of multiple M5-branes in flat space.

Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors