theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, in the context of

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...

, the

action Action may refer to: * Action (narrative), a literary mode * Action fiction, a type of genre fiction * Action game, a genre of video game Film * Action film, a genre of film * ''Action'' (1921 film), a film by John Ford * ''Action'' (1980 fil ...

for the '' N''=8 M2

branes In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. Branes are dynamical objects which can propagate through spacetime accordin ...

in full is (with some indices hidden): :

S = \intd\sigma^3

where is a generalisation of a

Lie bracket In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identit ...

which gives the group constants. The only known compatible solution however is: :

\eta \equiv \varepsilon^A_\mu B_\nu C_\tau

using the

Levi-Civita symbol In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers , for some ...

which is invariant under

SO(4) In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it is the special orthogonal group of order 4. In this article ''rotation'' means ''rotational dis ...

rotations. M5 branes can be introduced by using an infinite

symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...

. The action is named after

Jonathan Bagger Jonathan Anders Bagger (born August 7, 1955) is an American theoretical physicist, specializing in high energy physics and string theory. He is known for the Bagger–Lambert–Gustavsson action. Biography Bagger received his bachelor's degree i ...

, Neil Lambert, and Andreas Gustavsson.

Notes

References

''Lie 3-Algebra and Multiple M2-branes''
String theory {{string-theory-stub