M5brane

The M5-brane is an extended object in M-theory with a six-dimensional worldvolume (five spatial dimensions plus time) embedded in eleven-dimensional spacetime. It carries magnetic charge with respect to the three-form potential C3, and is magnetically dual to the M2-brane, coupling to the corresponding dual six-form potential C6. The field strength associated with the magnetic dual, F7, encodes the M5-brane’s flux.

The low-energy dynamics on a single M5-brane are described by a six-dimensional (2,0) superconformal field theory. Its field content includes a self-dual tensor gauge field (a chiral two-form) and five scalar fields corresponding to transverse fluctuations, together with fermions. There is no known conventional Lagrangian formulation for the interacting theory of multiple M5-branes; the abelian case can be described by formalisms such as the Pasti-Sorokin-Tonin approach, but a complete non-abelian generalization remains elusive.

Tension and charges of M-branes are set by the eleven-dimensional Planck length, lp. The M2-brane has tension T2 = 1/(2π)^2 lp^−3, while the M5-brane has tension T5 = 1/(2π)^5 lp^−6. An M2-brane can end on an M5-brane, with its boundary appearing as a self-dual string inside the M5 worldvolume.

When N M5-branes are coincident, the system gives rise to a six-dimensional (2,0) superconformal field theory of type A_{N−1}. The near-horizon geometry of such a stack is AdS7 × S4, providing a holographic description via AdS/CFT.

The M5-brane plays a central role in M-theory, dualities, and the study of strongly coupled six-dimensional quantum field theories, while many aspects of its non-abelian generalization remain active research.