Other meanings of M2-brane
Theoretical Physics
In M-theory, an M2-brane is a two-dimensional extended object, the fundamental membrane, whose tension is inversely proportional to the eleventh-dimensional gravitational coupling. It is the electric dual of the M5-brane and reduces to the type IIA superstring under dimensional compactification.
The M2-brane is the fundamental two-dimensional membrane of M-theory, the 11-dimensional quantum theory that unifies the five superstring theories. Its worldvolume is (2+1)-dimensional, and its tension scales as T ∝ 1/gs in string units, where gs is the string coupling.1 In the strong-coupling limit of type IIA string theory, the M2-brane wraps the 11th dimension, reducing to the fundamental string; conversely, unwrapped M2-branes appear as solitonic D2-branes in the weak-coupling limit. The M2-brane is the electric source of the 3-form gauge field C3 of 11D supergravity, while the M5-brane is its magnetic dual, coupling to the dual 6-form field.
The low-energy worldvolume theory of a single M2-brane is the maximally supersymmetric (8 supercharges) ABJM theory, a Chern–Simons gauge theory with gauge group U(N)×U(N) and level k, discovered in 2008 by Aharony, Bergman, Jafferis, and Maldacena.2 This theory describes N coincident M2-branes in an orbifold background and exhibits a strong–weak duality known as the AdS4/CFT3 correspondence, relating it to M-theory on AdS4×S7.3 The ABJM theory is a rare example of an interacting 3D conformal field theory with exact supersymmetry, and its partition function has been computed exactly via localization, providing non-perturbative checks of M-theory.4
Quantizing the M2-brane is notoriously difficult because its worldvolume theory is non-renormalizable in the traditional sense, and no perturbative string-like expansion exists. The light-cone gauge quantization of the supermembrane, pioneered by de Wit, Hoppe, and Nicolai in 1988, revealed a continuous spectrum, indicating a breakdown of conventional particle interpretation.5 Later work showed that the spectrum becomes discrete when the membrane is wrapped on a compact target space, but a full non-perturbative formulation remains elusive. The BFSS matrix model, proposed in 1997, conjectures that M-theory in the light-cone frame is described by the large-N limit of a supersymmetric matrix quantum mechanics, effectively treating M2-branes as composite objects of D0-branes.6
Beyond the standard lore, the M2-brane has several subtle features. Its worldvolume theory admits a class of BPS solutions called 'fuzzy spheres', where the transverse coordinates become non-commutative matrices, providing a geometric realization of the Myers effect.2 The M2-brane also plays a role in the AdS/CFT correspondence as the dual of Wilson loops in ABJM theory, and its scattering amplitudes exhibit hidden dual superconformal symmetry.4 Historically, the M2-brane was anticipated by the supermembrane of 11D supergravity, discovered by Bergshoeff, Sezgin, and Townsend in 1987, two years before the term 'M-theory' was coined.1 In compactifications to four dimensions, M2-branes can wrap calibrated cycles to produce effective strings, which are candidates for cosmic strings in cosmological models.
The M2-brane is a central object in M-theory, bridging string theory and 11-dimensional supergravity.
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