A Concise Review on M5-brane in Large C-Field Background

We give a concise review of recent developments of the M5-brane theory derived from the Bagger-Lambert model. It is a 6 dimensional supersymmetric self-dual gauge theory describing an M5-brane in a large constant $C$-field background. The non-Abelian gauge symmetry corresponds to diffeomorphisms preserving an exact 3-form on the worldvolume, which defines a Nambu-Poisson bracket. Various interesting geometric and algebraic properties of the theory are discussed.