M2-brane explained

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^[1] by requiring

(Poincare) _{3} x 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{align} ds ^{2} _{M 2} & = \left( 1+ (q)/(r ^{6}) \right) ^{- (2)/(3)} dx ^{\mu} dx ^{\nu} η _{\mu\nu} + \left( 1+ (q)/(r ^{6}) \right) ^{(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+ (q)/(r ^{6}) \right) ^{-1} , \mu =1 ,\ldots , 3 i =4 ,\ldots , 11 ,\end{align} where η 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.^[2]

See also

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

Notes and References

1. https://arxiv.org/abs/hep-th/9803116 K. Stelle, "BPS Branes in Supergravity"
2. https://arxiv.org/abs/hep-th/0509137 A. Miemiec, I. Schnakenburg "Basics of M-theory"