Astronomy: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

$\begin{array}{rl}d{s}_{M2}^2& ={(1+\frac{q}{r^6})}^{-\frac{2}{3}}d{x}^{\mu }d{x}^{\nu }{\eta }_{\mu \nu }+{(1+\frac{q}{r^6})}^{\frac{1}{3}}d{x}^{i}d{x}^j{\delta }_{ij}\\ F_{i{\mu }_1{\mu }_2{\mu }_3}& ={ϵ}_{{\mu }_1{\mu }_2{\mu }_3}{\partial }_i{(1+\frac{q}{r^6})}^{-1},\mu =1,\dots ,3i=4,\dots ,11,\end{array}$

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