M5branes

An M5-brane is a five-dimensional extended object in M-theory, spanning six spacetime dimensions. It carries magnetic charge with respect to the 3-form potential of eleven-dimensional supergravity and appears as a fundamental non-perturbative brane in the theory. The dynamics of multiple M5-branes give rise to rich six-dimensional physics that underpins various dualities and compactifications in string/M-theory.

The worldvolume theory of a single M5-brane consists, at low energies, of a six-dimensional (2,0) superconformal field theory. Its field content includes five scalar fields describing transverse fluctuations, fermions, and a self-dual two-form gauge field whose field strength H on the worldvolume satisfies a self-duality condition H = star H. Because of the self-duality, a conventional Lagrangian formulation is problematic; formulations such as the Pasti–Sorokin–Tonin approach provide a way to describe the theory, but even for a single brane the complete non-linear action is subtle.

For multiple M5-branes, the situation is more intricate. The interacting theory is believed to be a non-abelian generalization of the six‑dimensional (2,0) theory, often labeled by ADE types, but no complete Lagrangian description is known. The six-dimensional (2,0) theory is strongly coupled, and its precise formulation remains one of the central open issues in M-theory.

M5-branes play a key role in holography and compactifications. The near-horizon geometry of N coincident M5-branes is AdS7 × S4 in eleven-dimensional supergravity, with flux proportional to N, giving a holographic dual to the six-dimensional (2,0) CFT. Upon compactification, the six-dimensional theory yields lower-dimensional theories, such as five-dimensional maximally supersymmetric Yang-Mills theory on a circle and four-dimensional N=2 theories arising from wrapped M5-branes.