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{{string theory}}
In [[theoretical physics]], an '''M2-brane''', is a spatially extended mathematical object that appears in [[string theory]] and in related theories (e.g. [[M-theory]], [[F-theory]]). In particular, it is a solution of eleven-dimensional [[supergravity]] which possesses a three-dimensional [[World line|world volume]].

==Description==
The M2-brane solution can be found<ref>[http://arxiv.org/abs/hep-th/9803116 K. Stelle, "BPS Branes in Supergravity"]</ref> by requiring <math>(Poincare)_{3}\times SO(8)</math> symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a [[Metric tensor (general relativity)|metric]] and three-[[Differential form|form]] gauge field which, in isotropic coordinates, can be written as
: <math> \begin{align} ds^{2}_{M2} &= \left(1+\frac{q}{r^{6}}\right)^{-\frac{2}{3}}dx^{\mu} dx^{\nu}\eta_{\mu\nu} + \left(1+\frac{q}{r^{6}}\right)^{\frac{1}{3}}dx^{i}dx^{j}\delta_{ij} \\
F_{i\mu_{1}\mu_{2}\mu_{3}} &= \epsilon_{\mu_{1}\mu_{2}\mu_{3}} \partial_{i}\left(1+\frac{q}{r^6}\right)^{-1}, \quad \mu=1,\ldots ,3 \quad i=4,\ldots , 11,\end{align} </math>
where <math>\eta</math> is the [[Minkowski space|flat-space]] metric and the distinction has been made between world volume <math>x^\mu</math> and transverse <math>x^i</math> coordinates. The constant <math>q</math> is proportional to the [[Noether's theorem|charge]] of the brane which is given by the integral of <math>F</math> over the boundary of the transverse space of the brane.<ref>[http://arxiv.org/abs/hep-th/0509137 A. Miemiec, I. Schnakenburg "Basics of M-theory"]</ref>

==See also==
*[[String theory]]
*[[Membrane (M-theory)]]
*[[M-theory]]

==External links==
*http://www.superstringtheory.com/

==References==
{{Reflist}}

[[Category:String theory]]
[[Category:Physical cosmology]]

{{physics-stub}}

Analytically unramified ring - Revision history

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