M2-brane

In theoretical physics, an M2-brane, is a spatially extended mathematical object (brane) 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 volume.

Description

The M2-brane solution can be found by requiring $(Poincare)_{3}\times SO(8)$ symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three-form gauge field which, in isotropic coordinates, can be written as

${\begin{aligned}ds_{M2}^{2}&=\left(1+{\frac {q}{r^{6}}}\right)^{-{\frac {2}{3}}}dx^{\mu }dx^{\nu }\eta _{\mu \nu }+\left(1+{\frac {q}{r^{6}}}\right)^{\frac {1}{3}}dx^{i}dx^{j}\delta _{ij}\\F_{i\mu _{1}\mu _{2}\mu _{3}}&=\epsilon _{\mu _{1}\mu _{2}\mu _{3}}\partial _{i}\left(1+{\frac {q}{r^{6}}}\right)^{-1},\quad \mu =1,\ldots ,3\quad i=4,\ldots ,11,\end{aligned}}$

where $\eta$ is the flat-space metric and the distinction has been made between world volume $x^{\mu }$ and transverse $x^{i}$ coordinates. The constant $q$ is proportional to the charge of the brane which is given by the integral of $F$ over the boundary of the transverse space of the brane.

See also

• String theory
• Membrane (M-theory)
• M-theory