String theory |
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![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Calabi_yau_formatted.svg/100px-Calabi_yau_formatted.svg.png) |
Fundamental objects |
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- String
- Cosmic string
- Brane
- D-brane
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Perturbative theory |
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Non-perturbative results |
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- S-duality
- T-duality
- U-duality
- M-theory
- F-theory
- AdS/CFT correspondence
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Phenomenology |
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- Phenomenology
- Cosmology
- Landscape
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Mathematics |
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- Geometric Langlands correspondence
- Mirror symmetry
- Monstrous moonshine
- Vertex algebra
- K-theory
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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
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
![{\displaystyle {\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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd155b9d06b6849537650535632fa9ba0a0570a8)
where
is the flat-space metric and the distinction has been made between world volume
and transverse
coordinates. The constant
is proportional to the charge of the brane which is given by the integral of
over the boundary of the transverse space of the brane.[2]
See also
References
- ^ K. Stelle, "BPS Branes in Supergravity"
- ^ A. Miemiec, I. Schnakenburg "Basics of M-theory"
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